Presidents Joe Biden and Xi Jinping tried to take some heat out of their simmering superpower rivalry Monday, during a three-hour summit that found common ground on Ukraine but left little doubt that stark differences remain.

Biden emerged from the meeting proclaiming there need not be a new Cold War, as both leaders spoke of the desire to prevent high tensions from spilling over into conflict.

Xi told Biden that the two countries "share more, not less, common interests", according to a Chinese account of the meeting, sounding more conciliatory than the last three pandemic-filled years without face-to-face presidential meetings would suggest.

"The world expects that China and the United States will properly handle the relationship," Xi told him.

Trying to scotch the notion that China is bent on usurping the United States and remaking the world in its own authoritarian image, Xi reportedly said Beijing does not seek to challenge the United States or "change the existing international order".

On the pressing issue of Russia's war in Ukraine and President Vladimir Putin's veiled threats to use nuclear weapons, the pair agreed that nuclear war should not be fought and cannot be won, according to the White House.

They "underscored their opposition to the use or threat of use of nuclear weapons in Ukraine," the US added.

That common cause is likely to give Putin pause as he weighs how to turn the tide of a war that his regime's survival could hinge on.

But Biden and Xi's meeting was no kumbaya summit.

The two leaders notably clashed on the question of Taiwan's future.

Tensions have risen sharply over Taiwan, with China in August conducting major military exercises after a visit to the self-governing democracy, which it claims, by US House Speaker Nancy Pelosi.

Xi told Biden that Taiwan is the "first red line that must not be crossed in China-US relations," according to the Chinese foreign ministry statement.

Biden told Xi he opposed any changes on Taiwan -- after the US leader repeatedly indicated that Washington was ready to defend the island militarily.

And he raised US "objections" to China's "coercive and increasingly aggressive actions toward Taiwan, which undermine peace and stability across the Taiwan Strait and in the broader region, and jeopardise global prosperity," the White House said.

Biden also nudged China to rein in ally North Korea after a record-breaking spate of missile tests has raised fears that Pyongyang will soon carry out its seventh nuclear test, and said he was "confident China's not looking for North Korea to engage in further escalation".

In a sign of thawing ties, Biden announced that US Secretary of State Antony Blinken will visit China "to follow up on their discussions".

A senior State Department official, speaking on condition of anonymity, told AFP the two countries were working "to schedule a visit tentatively planned for early next year".

Xi's last in-person meeting with a US president was in 2019 with Donald Trump, who along with Biden identified China as a top international concern and the only potential challenger to US primacy on the world stage.

Although the meeting was the first time Xi and Biden have met as presidents, the pair have an unusually long history together.

By Biden's estimation, he spent 67 hours as vice president in person with Xi including on a 2011 trip to China aimed at better understanding China's then-leader-in-waiting, and a 2017 meeting in the final days of Barack Obama's administration.

On Tuesday, Xi will hold the first formal sitdown with an Australian leader since 2017, Prime Minister Anthony Albanese announced, following a concerted pressure campaign by Beijing against the close US ally.

He will also meet French President Emmanuel Macron, and Britain's new Prime Minister Rishi Sunak has said he also hopes to speak with the Chinese leader.

- Absent Putin -

Though he is engaging Xi, Biden has refused since the invasion of Ukraine to deal directly with Putin, who is conspicuously absent from the Bali summit.

The Kremlin cited scheduling issues and has instead sent longtime foreign minister, Sergei Lavrov, who arrived Sunday evening and underwent two health checks at a Bali hospital, according to an Indonesian health ministry official.

Lavrov, 72, denied reports that he was receiving treatment at a Bali hospital, telling Tass news agency that he was in his hotel preparing for the summit.

Lavrov's presence has thrown into question a customary G20 group photo and joint statement, with Russia sure to reject any explicit calls to end its invasion of Ukraine.

Debt relief in developing countries

The United States is pressing China and other G20 members to do more on debt relief for the world's poorest countries, a senior US official said Tuesday.

The issue will be highlighted in the final joint statement when the summit in the Indonesian resort island of Bali ends this week, the official said, but there will not be unanimity.

"What you're going to see in the G20 statement is that 19 members of the G20 came together to say this is a core, first-order issue that we need to take collective action with respect to, and you'll see that, you know, one country is still blocking progress," the official said, speaking on condition of anonymity.

He would not name the hold-out country but this appeared likely to be China, a massive creditor to poor countries around the world in a policy that Western countries have condemned as "debt traps" used to tighten Beijing's grip on the global economy.

The official mentioned similar opposition to joint agreement on restructuring such debts at the October meetings of the World Bank and International Monetary Fund.

The issue "will continue to be a topic of conversation between the US and China and within the G20", he said.

"We're seeing -- because of the stresses on the global economy, because of the food and energy security issues that we're facing, as well as the broader macro-economic headwinds in the globe -- that a set of emerging countries are finding themselves in pretty substantial distress when it comes to their debt burdens," the US official said.

"It is vital to find a way forward to provide those countries that relief, so they can ultimately begin growing again and get their citizens and their economy out from under the burden."

Debt relief will also be a concern in broader relations with China, which presidents Joe Biden and Xi Jinping sought to reinvigorate Monday at a meeting on the sidelines of the G20.

"I suspect that that will be a core topic that we continue engaging the PRC (China) on in the weeks and months ahead," the official said.

Biden and Xi ‘reassure’ world

Presidents Joe Biden and Xi Jinping both sought to lower the temperature between the United States and China during a rare summit, but few analysts expect any deeper easing of tensions.

After three hours of talks in Bali, Biden said there need not be a new Cold War between the two powers and Xi told him that China was not challenging the international order.

The White House said that Secretary of State Antony Blinken would visit China, the first visit by the top US diplomat in more than four years.

Biden "sent a reassuring message and the Chinese readout was positively glowing. That in itself shows both sides' interest in improving ties," said Yun Sun, director the China program at the Stimson Center in Washington.

But beyond a shared hope to avoid worst-case scenarios and direct clashes, she said the two powers had very different views on what a more stable relationship means, especially on the flashpoint of Taiwan.

"If we expect this summit to miraculously rescue this relationship and restore it to a better place, I think we need to see more concrete actions," she said.

Rui Zhong of the Wilson Center described the Bali summit as "maintenance work" and said even Blinken's visit could wind up being more about "treading water" than breakthroughs.

Moreover, for the first in-person summit between the two nations' presidents since 2019, each side had an interest in downplaying friction.

Biden and Xi were visiting for the Group of 20 summit, with host Indonesia inviting leaders of fellow Southeast Asian nations, several of which have maritime conflicts with China.

"For Xi, the perception of regional stability is still something that he would like to hold onto," Zhong said. "China growing and throwing its weight around has been a longheld concern of the smaller states of Southeast Asia."

"Xi gains nothing by coming off as excessively cold, inflexible and unnecessarily hawkish toward Biden, at least when face to face."

For Biden, the most pressing diplomatic priority has been reining in Russia over its invasion of Ukraine and he has trumpeted what he sees as China's wavering support for nominal ally Moscow, including a refusal to send weapons.

The White House said Xi agreed with Biden on "opposition to the use or threat of use of nuclear weapons in Ukraine," a phrase absent in China's statement.

- Deep suspicions -

Whatever their messaging to the world, both powers have deep suspicions of the other's intentions.

The Biden administration, in a national security strategy released last month, called China the only power that could challenge US primacy and sought a focus on ensuring the United States preserves a "competitive edge," including on new technology.

Deng Xiaoping, who spearheaded China's modernization in the 1980s, famously said his country should "bide time" and focus on its rise rather than immediately challenging other powers.

US policymakers widely see China as newly assertive under Xi, the country's most powerful leader in decades, who just secured a precedent-seeking third term.

Rush Doshi, a China advisor to Biden who took part in the Bali talks, wrote in a 2019 book while out of government that Xi saw historic opportunities due to what he viewed as Western decline, evidenced by the rise of Donald Trump, Britain's exit from the European Union and the pandemic response.

China's strategy involves "blunting and building efforts worldwide to displace the United States as the global leader," he wrote.

- Taiwan flashpoint -

An area where the relationship could quickly deteriorate is Taiwan, the self-governing democracy claimed by Beijing that stirs passion on both sides.

Biden's Republican rivals quickly attacked his diplomacy, with hawkish Senator Tom Cotton saying the "naive return to a policy of appeasement will hurt the United States, endanger Taiwan and further embolden Xi Jinping."

Biden told reporters he understood that Xi would not launch an "imminent" invasion of Taiwan, but Xi again warned about supporting Taiwan's "independence "

China carried out major military exercises in August after a defiant visit to Taipei by House Speaker Nancy Pelosi, second in line to the presidency.

Republican Kevin McCarthy, who may become the next speaker as votes are counted from last week's election, has made clear he would also visit Taiwan.

After Biden's reassurances, Xi "might have a little more room not to overreact" to a McCarthy visit, Sun said.

"But even then, I doubt the Chinese can afford not to react harshly."