Taiwan is considering extending its second highest COVID-19 alert that was due to expire at the end of the week, the health minister said on Monday, as he reported a further increase in domestic cases despite tighter social restrictions.

However, Health Minister Chen Shih-chung also said an infection peak was registered last Monday and should continue to decline.

"Judging from the trend of confirmed cases, it seems that the peak has reached a certain point," Chen said.

Taiwan has been battling a rise in infections after months of relative safety, shocking a population used to living with few restrictions, though the total case numbers remain low compared to some other parts of the world.

Chen announced another 590 new domestic COVID-19 cases, including 256 cases added to the totals for days over the past week or so as it continues to readjust its infection numbers following delays in reporting positive tests.

Chen said he hoped changes to the testing and reporting system would soon start to take effect so going forward there would be no need to adjust case tallies.

The government is also working to set up more test stations in "hot spots" across the island and has asked manufacturers to speed up the production of COVID-19 test kits.

Taiwan has reported 4,917 cases since the pandemic began, including 29 deaths.

Most of those infected in the current wave either have no or light symptoms. Northern Taiwan has been most badly affected, but cases have been reported across the island.