Prime Minister Junichiro Koizumi said Tuesday he sees no problem with current and former chief Cabinet secretaries Shinzo Abe and Yasuo Fukuda running in the ruling party's presidential race in September.

Koizumi, Abe and Fukuda all belong to the same faction in the Liberal Democratic Party -- the Mori faction, led by former Prime Minister Yoshihiro Mori.

Koizumi, meanwhile, backtracked and said it was possible he might ask the Diet to stay open beyond June 18, depending on how debate goes on a controversial bill to amend the 60-year-old basic education law with a section on patriotism. He had previously ruled out extending the legislative session.