Two countries lauded for keeping COVID-19 largely under wraps face uptick in cases. South Korea is closing schools and offering free tests, while Japan's prime minister is under fire for a travel incentive scheme.

The coronavirus has put South Korea "against the wall," President Moon Jae-in told the nation on Monday as schools were ordered to close under what's expected to become a "Phase 3" lockdown —  this year's first in Asia's fourth-largest economy.

South Korea since January has largely kept the global spread of the virus SARS-CoV-19 in check with residents proactively wearing face masks, curbs on travel and strict social distancing.

But its KDCA disease control center reported a daily record 1,030 new infections on Sunday and 718 on Monday. These numbers pale in comparison to those regularly clocked in western Europe or the Americas of late, but mark a distinct increase for South Korea itself. 

The largest outbreaks were detected in Seoul, surrounding Gyeonggi Province, and Incheon, South Korea's most densely populated metropolis of 25 million.  

"This is a crucial moment to devote all our virus control capabilities and administrative power to stopping the coronavirus," said Moon, adding: "Our back is against the wall."

Schools closing, new free testing centers opening

Prime Minister Chung Sye-kyun to health officials his government would "not hesitate to make the decision to upgrade to Phase 3 if it is considered necessary as it takes into account the opinions of related ministries, local governments and experts." 

From Tuesday, schools in Seoul and the surrounding area have been ordered to close, with classes moving online until the end of December. Hundreds of troops, police and officials also began a massive tracing effort to help track down virus carriers at 150 free testing centers being set up gradually around the capital — on top of more than 210 existing sites. 

Previously, anyone wanting a diagnosis on their own initiative had to pay if they tested negative.

Under a South Korean Phase 3 lockdown, only essential workers would be allowed into offices and gatherings would be capped at less than 10 people.

Underscoring the mood, South Koreans learned on Saturday that acclaimed but controversial film director Kim Ki-duk, 59, had died from COVID-19 in Latvia.

Under-fire Suga puts Tokyo domestic tourism campaign on ice

In Japan, meanwhile, Prime Minister Yoshihide Suga on Monday bowed to pressure to halt a system of subsidies for domestic travelers after Japanese authorities reported a single-day record of more than 3,000 new coronavirus cases on Saturday.

As winter set in, new cases occurred in Tokyo, Osaka and the northern island of Hokkaido, with the prime minister keen to avoid restrictions, citing economic considerations.

However, his government did later announce that the "Go To Travel" campaign designed to reinvigorate domestic travel and tourism would be put on hold amid waning public support his pandemic handling.

Japan hopes next year to stage the postponed summer Olympics.

Fumie Sakamoto, infection control manager at St Luke's International Hospital in Tokyo, urged more testing in and around the capital.

The positivity rate for Tokyo is now over 6%, so we should be doing a bit more testing to bring the number down," said Sakamoto.