China's official Purchasing Managers' Index rose to 52 in March from a collapse to a record low of 35.7 in February, but analysts cautioned the index might overstate the true improvement as firms could be reporting expansion after a forced stoppage.
Many also warn that manufacturers and overall economic activity will remain under pressure as the virus continues to spread rapidly around the globe, while governments and central banks continue in their attempts to cushion its impact.
"Asia, having led the world into the coronavirus epidemic, appears to be showing signs of a tentative, if uneven, recovery," OANDA analyst Jeffrey Halley wrote in a note.
Indonesian shares rose as much as 3.5%, underpinned by consumer staples and financials.
Indonesian President Joko Widodo said on Monday he planned stricter rules on mobility and social distancing. The country confirmed 130 new virus infections on Sunday, taking the total to 1,285.
Singaporean stocks bounced back, rising as much as 3% in early trade. Index heavyweights Jardine Matheson Holdings and Jardine Strategic Holdings were both up more than 5%.
Thai shares rose up to 2.4%, with financial and energy stocks leading the gains.
Thailand's finance minister said on Monday the new stimulus package to counter the impact of the pandemic would be worth more than 500 billion baht ($15.3 billion), while the central bank said it had further expanded the scope of liquidity support.
Vietnamese equities gained on financials. Prime Minister Nguyen Xuan Phuc on Monday ordered the suspension of public transport services to curb the spread of the virus, which is known to have infected 203 people in the country.
Philippine stocks added up to 4%, with big caps SM Investments and Ayala Land rising more than 3% each.
By Arundhati Dutta