Asian markets mostly rose Monday but investor optimism over the global recovery was being kept in check by worries over the spread of the Delta Covid variant as well as China's regulatory crackdown.

Signs that US lawmakers were edging towards agreement on Joe Biden's $1 trillion infrastructure bill were unable to provide much of a boost, while eyes are on the release of US jobs data at the end of the week as firms struggle to fill positions despite unemployment remaining high.

In the latest sign that the global outlook is upbeat, figures last week showed the US economy had returned to its pre-pandemic level -- though at a slower pace than expected -- while the eurozone expanded at a much better rate than forecast.

However, observers said the rally that world markets have enjoyed for much of the past year was sputtering as investors grow increasingly concerned about spiking inflation that many have warned could force central banks to taper their ultra-loose monetary policies.

Added to that is the slow vaccination programmes in some countries and rapid spread of the Delta variant that has led to the reimposition of lockdowns and other containment measures.

In early trade, Tokyo, Hong Kong, Shanghai, Sydney, Seoul, Wellington, Taipei and Manila rose but Singapore and Jakarta fell.

"Shares remain at risk of a short-term correction or volatility as coronavirus cases rise globally, the inflation scare continues and as we come into seasonally weaker months, but surging company profits in the US and lower bond yields are providing support," said Shane Oliver at AMP Capital.

Nervous traders are keeping tabs on China after authorities last week embarked on a crackdown on the country's private tuition firms as well as the tech and property sectors.

The moves raised concern that other industries could be next, despite officials and state media trying to calm markets in the face of a rout.

Afterpay soars  

On Friday, tech firms were told by authorities to conduct "deep self-examination" over issues including data security and user rights as they tighten the leash on big corporations citing national security and antitrust concerns.

Major names including Alibaba, Tencent, ByteDance and Pinduoduo were among more than 20 firms summoned to a meeting with a department of the Ministry of Industry and Information Technology where they were told to scrutinise their approach to user rights infringement, data security and violations of resource management regulations.

Tencent fell more than two percent in Hong Kong, though Alibaba rose more than one percent.

Still, CICC strategists led by Hanfeng Wang wrote in a note: "Last week's selloff may be overdone from a technical, near-term perspective.

"Parts of the market are ripe for entry."

Traders are also watching developments in Washington, where the Senate looks to be on course to pass Biden's infrastructure bill, which will provide an extra jolt to the world's top economy, adding to the president's $1.9 trillion stimulus earlier in the year.

Lawmakers finalised the bipartisan legislation on Sunday after a special weekend session, and Senate Majority Leader Chuck Schumer said: "I believe the Senate can process relevant amendments and pass this bill in a matter of days."

The bill includes huge spending on roads and bridges, the electric grid, transit, broadband and drinking water.

Biden is also aiming to pass an ambitious $3.5-trillion budget package that includes once-in-a-generation spending on health care, education, social welfare and climate action.

In company news, Afterpay shares surged more than 20 percent after US digital payments platform Square Inc., led by Twitter founder Jack Dorsey, said it would buy the Sydney-listed buy-now, pay-later company for US$29 billion.