The Philippine benchmark closed 0.6% higher and led gains in the region, having lost 3% last week.
Gains were dominated by index heavyweights such as Ayala Corp and SM Investments, which gained 0.7% and 2.3%, respectively.
In a move to cushion the economic fallout from the epidemic, China's central bank lowered the interest rate on its medium-term loans, paving the way for a cut in the country's benchmark loan prime rate, set to be announced on Thursday.
The number of reported new virus cases in China's Hubei province rose on Monday, after two days of falls, while the death toll across mainland China reached 1,770.
Singaporean stocks closed slightly lower after the city-state cut its 2020 growth outlook and flagged the possibility of recession on the likely impact from the outbreak. Singapore is expected to roll out a hefty stimulus package at its annual budget on Tuesday.
"A strong fiscal response is expected to mitigate the impact of the virus outbreak," Irvin Seah, a senior economist at DBS Group Research wrote in a note, adding that the city-state could further loosen monetary policy if growth prospects worsen.
Malaysian shares fell 0.5%, pulled lower by a drop in telecom stocks.
The Thai index was little changed after data showed the economy grew at its weakest pace in five years in 2019, adding pressure on its central bank to cut rates.
However, Advanced Info Service Pcl gained nearly 5% after it emerged as the biggest winner at Thailand's 5G spectrum auctions on Sunday, with 23 licences.
Indonesian equities were flat. The country's trade gap widened sharply in January as falling metals prices weighed on exports, data showed on Monday.
By Arundhati Dutta