TAIPEI, April 21 (Reuters) - Taiwan's government has approved a second COVID-19 booster vaccine dose for those 65 and older, and third boosters for the immunocompromised, as it looks to step up its fight against a spike in domestic infections.

While Taiwan is dealing with a rise in local cases, the numbers overall remain small - 13,164 since Jan. 1 - and just four people have died, with more than 99% of those infected reporting either minor or no symptoms.

Taiwan's Centres for Disease Control said late Wednesday it had approved second booster shots for the elderly, as well as residents of long-term care facilities.

People with compromised immune systems, including dialysis patients and those who have received organ transplants, are approved for third booster shots, it added.

Those getting their second or third booster should get them at least five months after their last shot, and can choose among the Moderna Inc, Pfizer/BioNTech, Taiwan-made Medigen or Novavax brands, it said.

Taiwan has yet to receive any Novavax vaccines.

South Korea has approved a second booster shot for people over 60 and Singapore has said a second booster dose is planned for those 80 and older.

About 80% of Taiwan's 23 million people are now double vaccinated and more than half have had a booster dose, while mask-wearing mandates continue.

The government has warned that a further rise in cases is expected, driven by the more infectious Omicron variant. (Reporting by Ben Blanchard. Editing by Gerry Doyle)