Tamaki said he would ask his party members if he should resign as leader of the Democratic Party for the People (DPP).
"I apologise for the trouble caused," he told reporters at a hastily called news conference after tabloid SmartFlash reported the affair on Monday.
"The facts reported this morning are basically true," he said. SmartFlash reported that Tamaki, 55, and a 39-year-old model and entertainer rendezvoused in July and October. It published a photo of Tamaki in a grey hoodie as he emerged from a bar, followed 20 minutes later by the woman.
"My wife had told me, 'you can't protect the country if you can't protect the person closest to you.' I will etch those words in my mind once again, reflect on my action and do my best to work in a way that is in the best interests of the country and to realise policies," Tamaki said.
Japanese lawmakers are set to decide at a special parliamentary session on Monday whether Prime Minister Shigeru Ishiba should stay as the country's premier after his scandal-tarnished coalition lost its parliamentary majority in an election last month.
Tamaki has previously said his party members would not vote for Ishiba but could offer support to the prime minister's Liberal Democratic Party on a policy-by-policy basis.
