Stock prices in Australia led gains among the region's bigger markets with the S&P/ASX 200 up about 2.1% as shares of the country's large banks were bought. Australia & New Zealand Banking Group shares gained 3.63%, the Commonwealth Bank of Australia shares added 2.65%, Westpac shares 3.74% and paper in National Australia Bank added 3.26%.
Hong Kong's Hang Seng index rose 1.57% in early trade following its return to trade from holidays last week - with shares of HSBC rising more than 4%.
In Japan, the Nikkei 225 index rose 1.28% in morning trade. South Korea's Kospi added 1.06%.
Markets in China are closed Monday for a holiday.
Elsewhere in the world markets recovered following falls after U.S. President Donald Trump's COVID-19 diagnosis Friday. Reports of Trump being discharged later calmed markets.
The 74-year-old U.S. president was flown to hospital late last week after he was found to be positive for the virus. Doctors on Monday said Trump was responding well to treatment and that he could potentially return to the White House within days.
The news helped U.S. futures in early trading in Asia. U.S. S&P 500 e-mini futures bounced by about 0.82%, while NASDAQ futures rose 1.11%. MSCI's index of Asia-Pacific shares also increased slightly by 0.63%.
"Equities and other risk-on traders should be well supported by easing concerns about Trump's health. For the dollar, the impact is not quite as clear cut. It should fall against most currencies due to an increase in risk appetite," analysts at Tokyo-based IG Securities had pointed out.
Market participants were surprised late last week after Trump announced he and his wife had tested positive for the coronavirus. This saw share prices slide - eclipsing the anticipated job loss report for September. The S&P 500 closed 32 points lower, or 0.96%. The Dow Jones fell 134 points, while the Nasdaq composite closed down 251 points - or 2.2%.
With just a few weeks left until the next U.S. Presidential Elections, Trump's contraction of the virus has become yet another source of market volatility. The health of the president of the world's largest economy and the prolonged pandemic has made it very difficult for investors to predict the direction of the markets.
Yields on benchmark 10-year Treasurys rose to 0.7104% and the yield curve steepened -- a sign that the many participants are comfortable taking on more risk.
Gold was little changed at $1,898.90. In oil, Brent crude futures rose 1.22% to $39.75 a barrel while U.S. crude futures gained 1.46% to $37.59 a barrel.
