TOKYO—More than a third of Japan's ruling party lawmakers protested the premier's push to promptly restart the nation's nuclear reactors, threatening to undermine his leadership as he struggles to gain party support for another critical issue—the passage of a sales tax increase proposal this month.

A group of 117 Democratic Party of Japan lawmakers on Tuesday submitted to Prime Minister Yoshihiko Noda a petition to exercise "greater caution" over restarting two reactors at Kansai Electric Power Co.'s Oi nuclear power plant....