TOKYO — Voters in Tokyo head to the ballot box Sunday to deliver their verdict on Shinzo Abe’s ruling party after scandals sent support for the prime minister tumbling.

Polls show his long-dominant Liberal Democratic Party (LDP) could suffer a beating at the hands of an upstart party led by Governor Yuriko Koike in elections for Tokyo’s political assembly. Ms. Koike, who defected from the LDP only last month, is one of Japan’s most popular politicians.

A loss in Tokyo could stir up criticism of Mr. Abe within his party, where potential rivals are positioning themselves to end his run as Japan’s third-longest serving premier since World War II. It could also hurt the party’s chances in a national election due next year. In 2009, a big loss for the LDP in Tokyo preceded a landslide general election defeat months later.

Voting began at 7 a.m. and runs until 8 p.m. in the city of 13.7 million, which accounts for about a fifth of Japan’s economy. Once ballot booths close, public broadcaster NHK will provide projections of the results based on exit polls.

Turnout as of 3 p.m. was 23.6%, 2.1 percentage points up from the previous election, Kyodo News said, citing the Tokyo government’s election administration commission. A higher turnout is seen by analysts as negative for the LDP.

A survey published Wednesday by Jiji news saw Ms. Koike’s Tomin First (Tokyo Residents First) party and affiliated groups gaining a majority of the 127 seats. Immediately before the election, Ms. Koike’s party had only six seats in the Tokyo assembly, compared with 57 for Mr. Abe’s LDP, according to the assembly’s office.

POPULIST PLATFORM

Ms. Koike has campaigned on a platform of open government, cutting wasteful spending and a pledge to bring more women into the assembly. The LDP has sought to portray her as indecisive for delaying the relocation of the iconic Tsukiji fish market over pollution concerns and insisting on reviewing the ballooning cost of the 2020 Olympics.

Mr. Abe, 62, has seen his popularity suffer due to ministerial gaffes and allegations of cronyism over government support given to a school run by one of his close friends. More popular colleagues such as Shinjiro Koizumi, the 36-year-old son of a former premier, have taken a prominent role in the Tokyo campaign.

In a speech in Tokyo on Wednesday, Mr. Abe apologized for the angry exchanges over scandals that dominated the last parliamentary session, and vowed to fight on. “A castle that takes three years to build can be destroyed in a day,” he said.

Demonstrators heckled Mr. Abe during his final stump speech on Saturday evening, calling for him to “resign” or “go home,” local media said.

Ms. Koike, 64, is a former television journalist fluent in English and Arabic who has served as environment minister and defense minister, as well as a ruling party executive. A big win would give her momentum to take her more populist message on to the national stage.

In the 2009 Tokyo poll, the LDP and its coalition partner Komeito lost their dominant position in the assembly — months before a resounding defeat to the Democratic Party of Japan in a general election that led to more than three years in opposition. This time, however, Mr. Abe doesn’t have to call a vote until December 2018, a few months after the LDP is due for a formal leadership election. — Bloomberg