Asian markets mostly rose Monday following another Wall Street record sparked by a blockbuster U.S. jobs report that reaffirmed the country's recovery was on track, while oil prices dipped as top producers struggled to reach a deal on lifting output.

All three main indexes in New York finished the week at a fresh peak in reaction to data showing far more people than expected were employed last month, as the world's top economy continues to race out of last year's pandemic-induced recession.

The Labor Department report was seen as providing the best of both worlds for investors as it also showed the unemployment rate ticking up slightly, tempering worries that the Federal Reserve will have to rein in its ultra-loose monetary policy sooner to prevent the economy from overheating.

"Overall, the level of payrolls is still 6.8 million below pre-pandemic February 2020 levels and is still below the level of substantial progress needed by the Fed," said National Australia Bank's Tapas Strickland. "As such there is nothing in this report for the Fed to become hawkish about."

The healthy advances on Wall Street provided Asian traders with a platform, and most markets extended the rally.

Sydney, Seoul, Singapore, Wellington, Manila and Jakarta all rose.

Shanghai edged higher but Hong Kong was flat, with tech firms taking a hit again after China at the weekend ordering ride-hailing giant Didi to be removed from app stores after a probe found "serious violation" of data collection regulations.

Tencent fell more than one percent in Hong Kong while Alibaba shed more than two percent. 

SoftBank, a major investor in Didi, tanked more than five percent in Tokyo, where the Nikkei was also in negative territory.

Still, the general feeling is that equities are on course for more gains this year as central banks maintain their accommodative policies and governments push out stimulus measures. 

That, along with the rollout of vaccines, is helping offset concerns about rising cases of the more transmissible Delta virus variant. 

"Markets are priced for the continuation of a scenario that could not be better constructed," Chris Iggo, of AXA Investment Managers, said. "Investors are living with risks that are seen to be manageable while growth and the technical set-up of our financial system is rewarding capital allocated to risk."

Traders are now awaiting the release this week of minutes of the Fed's most recent policy meeting, hoping for an indication about its plans for tightening policy in light of the strong recovery.

Oil markets were down slightly as the United Arab Emirates battled with OPEC and other producers over the rate and time of lifting output.

Officials have labored for days over an agreement to pump more as demand picks up with the global recovery and supplies shrink, with fears that failure to find common ground could send prices soaring. 

Prices remain around levels not seen since 2018.