Investors appear to be looking past the outbreak to a recovery despite rising infection numbers in the United States, Brazil and some other countries.
Forecasters warn the the latest market buoyancy might be premature and a return to normal could be some way off.
Market sentiment will likely remain fragile as investors weigh government stimulus plans against rising US-Chinese tension and poor economic data, said Riki Ogawa of Mizuho Bank in a report.
The Shanghai Composite Index rose 0.2 per cent to 2,874.89 and Tokyo's Nikkei 225 gained 0.3 per cent to 20,105.84.
The Hang Seng in Hong Kong advanced 0.1 per cent to 23,819.26.
The Kospi in Seoul was 0.5 per cent higher at 1,935.73 and Australia's S&P-ASX 200 gained 1.4 per cent to 5,478.10. Markets in New Zealand and Singapore also advanced.
Federal Reserve Chair Jerome Powell expressed optimism Sunday that the US economy can begin to rebound in the second half, assuming the coronavirus doesn't erupt in a second wave, but said a full recovery won't likely be possible before the arrival of a vaccine.
That appeared to encourage investors who are looking for signs of when global economies might return to normal.
In an interview with CBS's 60 Minutes, Powell said the US economy was fundamentally healthy before the virus forced widespread business shutdowns and tens of millions of layoffs. Once the outbreak has been contained, he said, the economy should be able to rebound substantially.
The US downturn was the result of an external event instead of problems such as the financial instabilities that led to the 2008 crisis, which may mean we can get back to a healthy economy fairly quickly, Powell said.
Powell and Treasury Secretary Steven Mnuchin are due to appear Thursday before a Senate panel to report on recovery efforts.
Expect policymakers to strike a more cautious tone, emphasizing that we are not out of the woods yet and that more will be more stimulus in the offing, Stephen Innes of AxiCorp said in a report.
Meanwhile, Japan's government reported Monday the world's third-largest economy contracted by 0.9 per cent in the three months ending in March compared with the previous quarter.
That sharp fall suggests there is much worse to come in the current quarter, Tom Learmouth of Capital Economics said in a report.
On Wall Street, US stocks turned in their biggest weekly loss in nearly two months.
The S&P 500 index rose 11.20 points to 2,863.70. It ended down 2.3 per cent for the week.
The Dow Jones Industrial Average gained 0.3 per cent to 23,685.42.
The Nasdaq composite added 0.8 per cent to 9,014.56.
Meanwhile, the White House added to trade uncertainty by tightening restrictions on Huawei Technologies Ltd.
American officials say Huawei, one of the biggest makers of smartphones and network equipment, is a security risk, which the company denies.
Washington said non-US companies that make processor chips for Huawei must obtain permission to use American technology, a move that threatens to disrupt sales.
Huawei warned earlier that additional US sanctions on the company might trigger Chinese government retaliation against American enterprises.
European governments are reopening factories, shops and other businesses but forecasters warn an economic recovery could be slow.
Chinese data reported last week showed manufacturing and auto sales are recovering but consumer spending, the biggest driver of growth for the second-largest global economy, is still declining amid widespread job losses.
In energy markets, benchmark US crude gained USD 1.23 to USD 30.75 per barrel in electronic trading on the New York Mercantile Exchange.
The contract rose USD 1.87 to USD 29.43 on Friday. Brent crude, used to price international oils, advanced USD 1.31 to USD 33.81 per barrel in London. It rose USD 1.37 the previous session to USD 32.50.
The dollar gained to 107.10 yen from Friday's 107.08 yen. The euro was unchanged at USD 1.0828.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)
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