Chiu Kuo-cheng verbally tendered his resignation to Tsai on Thursday night over "matters involving his family", presidential spokeswoman Olivia Lin said in a statement.

"Considering the current complex regional security situation and the transitional period of the government team, the President believes that the minister should stay in his post to ensure the stability and comprehensiveness of various important national defence affairs," she said.

Lin added that relevant agencies will investigate "the matters" in accordance with the law, without providing any details.

Tsai is due to step down on May 20 after serving the maximum two four-year terms.

She will be succeeded by her current deputy Lai Ching-te, who won the January 13 presidential elections.

The defence ministry also said in a statement on Friday that Chiu orally tendered his resignation over "family matters" but was asked by the president to stay.

"Minister Chiu will follow the instructions and fulfil his duties... during the handover period," it said, adding that his family "will fully cooperate" with the investigation.

Local media reported Thursday that Chiu's son, who works for the National Security Bureau, allegedly hired sex workers.