Taiwan said earlier this month it would set up a dedicated office to help those thinking of leaving Hong Kong as Beijing tightens its grip on the former British colony, including planned new national security legislation.
The new office begins operations on the sensitive date of July 1, the day Hong Kong returned to Chinese rule in 1997 with the promise of continued, wide-ranging freedoms under China's "one country, two systems" formula.
Taiwan largely closed its borders in mid-March to prevent the spread of the coronavirus, meaning anyone who wished to come to the island from Hong Kong would have found it very difficult.
In a statement, Taiwan's Central Epidemic Command Centre said that from Monday, Hong Kong people who wish to travel to Taiwan for "special humanitarian considerations" would be allowed to apply to be let in, though they will have to prove before they come they do not have the coronavirus.
They will also have to complete 14 days of quarantine, as do all arrivals into Taiwan.
China, which claims democratic Taiwan as its own territory, has condemned Taipei's government for offering to help people from Hong Kong, which was hit by months of sometimes violent anti-China, pro-democracy unrest before coronavirus curbs were introduced. China denies meddling in Hong Kong's affairs.
Taiwan has been extremely successful at controlling the spread of the virus, thanks to early and effective prevention work, and has never gone into complete lockdown, unlike other countries around the world.
The epidemic command centre said in a separate statement that from Thursday it will also re-allow some passengers to transit via Taipei's main international airport, though they will not be allowed to leave the airport and will be kept separate from other passengers. (Reporting by Ben Blanchard; Editing by Nick Macfie)

epa08490829 A general view of the Taipei Songshan Airport in Taipei, Taiwan, 16 June 2020 (issued on 17 June 2020). On 17 June, Taiwan announced it will ease border control caused by Covid-19 starting 22 June. Under the new rule, invited business people from low-risk and medium low-risk countries/regions can visit Taiwan if their trip is not longer than three months, they have negative Covid-19 test result within three days before flying to Taiwan, and they have not visited other countries or regions within 14 days before flying to Taiwan. Low-risk countries/regions are New Zealand, Australia, Macau, Palau, Fiji, Brunei, Vietnam, Hong Kong, Thailand, Mongolia and Bhutan. Medium low-risk countries/regions are South Korea, Japan, Malaysia and Singapore. EPA-EFE/DAVID CHANG