Japan has avoided mass infections but a record surge in cases during the past week in Tokyo and other urban centers has experts worried the country faces a second wave.
Vietnam is evacuating 80,000 people, mostly local tourists, from the central city of Danang.
The move came after three residents tested positive for the coronavirus at the weekend, the government said on Monday.
The Southeast Asian country is back on high alert after the government on Saturday confirmed its first community infections since April, and another three cases on Sunday, all in Danang.
In the Philippines, President Rodrigo Duterte is expected to focus on Covid-19 and the economy in his annual State of the Nation Address on Monday.
Manila is weighing whether to re-impose stricter lockdown measures after easing them saw a dramatic surge in infections and deaths, with 62,326 cases reported since the first lockdown was relaxed June 1.
Elsewhere in Southeast Asia, Malaysia is expected to announce new measures to contain the outbreak.
Authorities are struggling to contain more than a dozen new clusters that have appeared since curbs were lifted last month.
Indonesia is expected to report its 100,000th case on Monday, having surpassed China with the highest number of cases and deaths in East Asia.
North Korean state media reported on the weekend that the border town of Kaesong was in lockdown after a person who defected to South Korea three years ago returned this month with symptoms of Covid-19.
If confirmed, it would be the first case officially acknowledged by North Korean authorities.
South Korea has reported more than 14,000 cases and 298 deaths from the pandemic. Saturday's 113 infections were the highest on a single day since March 31.
Papua New Guinea halted entry for travelers from Monday, except those arriving by air, as it tightens curbs against infections that have more than doubled over the past week.