Liberal Democratic Party lawmaker Itsunori Onodera, 49, told reporters Thursday he will not run for party president.
Onodera, a member of the House of Representatives, had been considered a possible contender for the LDP presidency, which will be decided on Sept. 28.
Onodera said he wanted to avoid a scenario in which many young lawmakers are running at the same time because that would make it difficult for each of them to get the required number of signatures from fellow party members to file a candidacy.
Meanwhile, Nobutaka Machimura, 64, who heads the largest LDP faction, told members at one of its regular meetings Thursday that he doesn't intend to seek the post either.
Those who have already declared they intend to run include former Finance Minister Sadakazu Tanigaki, 64, and 46-year-old Lower House member Taro Kono of Kanagawa Prefecture.
On Thursday, Tanigaki visited LDP members in both chambers of the Diet at the office building for lawmakers in Nagata-cho, seeking support for his bid for the presidency.
Former farm minister Shigeru Ishiba, who was considered a potential candidate, dropped out Wednesday, saying the party should focus on preparing for next July's Upper House election instead.
"There aren't many days left before the Upper House election. We don't have time for a power struggle over the leadership," Ishiba said.