TAIPEI, April 11 (Reuters) - Taiwan has ordered 700,000 units of Pfizer Inc's anti-viral COVID-19 pill Paxlovid, its health minister said on Monday, amid a steady increase in the number of infections as the government pledges to gradually reopen its borders.

Taiwan has kept the pandemic well under control thanks to strict and early control measures. But daily infections have been rising in recent weeks, with 439 new cases reported on Monday, the second highest daily increase this year.

The government is on alert even though the numbers remain comparatively low and health ministry data shows 99.6% of those infected so far this year showed mild or no symptoms.

Health Minister Chen Shih-chung said the pills ordered would be enough to cover 3% of Taiwan's population, with half of them due to arrive in the second quarter this year.

"The medication could prevent serious illness and is very helpful for overall pandemic prevention," Chen told reporters.

Since the beginning of this year, Taiwan has reported 3,976 domestic cases, with only 13 people classified as being seriously ill and just two deaths.

Taiwan has maintained mandatory mask wearing and almost 80% of the population have had two vaccine shots while more than 50% have had three.

It is gradually relaxing quarantine rules for all arrivals on the island, but most foreigners apart from residents are still barred from entry.

(Reporting By Yimou Lee; editing by Philippa Fletcher)