US Secretary of State Antony Blinken headed to Jordan Wednesday on the last leg of a Mideast tour that aims to shore up an Egypt-brokered ceasefire between Israel and Palestinian militants in Gaza.

After meeting Egyptian President Abdel Fattah al-Sisi -- whom he praised for helping bring an end to the intense violence "relatively quickly" -- he departed for Jordan for talks with King Abdullah II.

The US top diplomat already met Tuesday with Israeli and Palestinian leaders, to throw Washington's support behind the truce that ended 11 days of heavy Israeli bombing of Gaza and rocket fire from the enclave into Israel. 

After talks with Palestinian president Mahmud Abbas at his headquarters in the Israeli-occupied West Bank, Blinken vowed to rebuild US relations with the Palestinians by reopening a consulate in Jerusalem, as well as giving millions in aid for the war-battered Gaza Strip.

The announcements signalled a break with US policy under former president Donald Trump, who had shuttered the diplomatic mission for Palestinians in 2019 and slashed aid to the Palestinian Authority.

In the long term, Blinken evoked the "possibility of resuming the effort to achieve a two-state solution, which we continue to believe is the only way to truly assure Israel's future as a Jewish and democratic state, and of course to give the Palestinians the state they're entitled to".

After meeting Israeli Prime Minister Benjamin Netanyahu, he reiterated support for Israel's right to defend itself against rocket attacks by Gaza's Hamas rulers, adding that they must not benefit from the reconstruction aid.

Rebuilding Gaza 

On Wednesday, he met with Sisi, with Blinken later saying both "believe strongly that Palestinians and Israelis deserve equally to live in safety and security", and that "Egypt is vital to these aspirations".

Unlike the United States and many European governments, which boycott Gaza's ruling Hamas movement as a terror group, Egypt maintains regular contacts.

Egypt was also the first Arab country to sign a peace treaty with Israel in 1979, with Jordan following suit in 1994.

Cairo has sent delegations to both Tel Aviv and Gaza to watch over the implementation of the ceasefire, and has also been coordinating international relief and reconstruction aid for the Palestinian territory, which has been under Israeli blockade for nearly 15 years.

Blinken said Wednesday the United Sates was in the process of providing more than $360 million in assistance to the Palestinian people, including $250 million announced in March and April.

On top of that, the administration intended to provide $75 million in additional aid to the Palestinians, as well as $5.5 million in immediate disaster assistance for Gaza, and nearly $33 million for an emergency humanitarian appeal by the UN agency for Palestinian refugees.

"All of these funds will be administered in a way that benefits the Palestinian people -- not Hamas, which has only brought misery and despair to Gaza," Blinken said.

Last week, Sisi pledged $500 million to help reconstruction efforts in Gaza.

Britain's Raab in Jerusalem 

British Foreign Secretary Dominic Raab meanwhile travelled to Jerusalem Wednesday, urging an end to the "cycle of violence" through a two-state solution to the Israeli-Palestinian conflict. 

The latest military escalation started after clashes in Jerusalem's Al-Aqsa mosque compound, Islam's third holiest site, which is also revered by Jews as the Temple Mount.

Israeli security forces had moved in on Palestinian worshippers there towards the end of the Muslim holy month of Ramadan.

They had also sought to quell protests against the threatened eviction of Palestinian families from homes in the east Jerusalem neighbourhood of Sheikh Jarrah to make way for Jewish settlers.

Israeli air strikes and artillery fire on Gaza killed 254 Palestinians, including 66 children, and wounded more than 1,900 people in 11 days of conflict from May 10, the health ministry in Gaza says.

Rocket and other fire from Gaza claimed 12 lives in Israel, including one child and an Arab-Israeli teenager, an Israeli soldier, one Indian national and two Thai workers, medics say. Some 357 people in Israel were wounded.

The UN Human Rights Council will hold a special session focused on Israel Thursday, to consider launching a broad, international investigation into abuses during the violence.