Japanese Prime Minister Shigeru Ishiba was on Monday pitted against the main opposition chief as parliament votes to appoint the nation's leader.

Ishiba, 67, is expected to keep his job, but with a fragile grip on power after his ruling coalition lost its majority in a snap election last month.

The former defense minister, who took office six weeks ago, had hoped to shore up his mandate as leader of the ruling Liberal Democratic Party (LDP) in the 27 October polls.

Instead, voters unhappy with inflation and a slush fund scandal that helped sink his predecessor Fumio Kishida delivered the party its worst result since 2009, which could cause political gridlock in a hung parliament.

Ishiba is reportedly trying to arrange a meeting with US president-elect Donald Trump later this month, around the time he travels to Peru for an economic summit.

Lawmakers in the powerful lower house convened on Monday afternoon for a special four-day session to nominate the prime minister, a necessary step after a general election.

The conservative LDP and its junior coalition party remain the largest bloc in the 465-seat lower house, where the opposition parties are deeply divided on key issues.

So, Ishiba is expected to lead a minority government after a run-off — the first since 1994 — with Yoshihiko Noda of the Constitutional Democratic Party of Japan (CDP).

Affair scandal

"In order to stay in power, Ishiba needs to pass the government budget this winter. It will mean the LDP will have to concede some of its policies to seek cooperation from others," Tomoaki Iwai, professor emeritus at Nihon University, told AFP.

To have enough sway to pass legislation going forward, the ruling bloc has asked for help from the Democratic Party for the People (DPP), a small centrist group.

The DPP has agreed to cooperate on a vote-by-vote basis while staying out of the coalition. In talks with the LDP, it has demanded tax cuts and energy subsidies that economists say would slash the government's revenues.

In a twist, DPP head Yuichiro Tamaki on Monday admitted to an extra-marital affair reported by a tabloid.

"I apologize for causing such a disturbance," he told reporters. His party later reportedly decided to keep him on as leader.

Along with these negotiations, Ishiba must also contend with discontent within his party, which lost dozens of seats — including ministers — in the election.

"Unless he improves his public support, those inside the LDP may start saying they cannot fight the upper house election under Ishiba" and look for another leader, Iwai added.

The public votes in the upper house election in July, and Noda vowed last week that the CDP would "work hard so we will make significant gains in the upper house election".

Trump 'headache'

Approval ratings for Ishiba's government are just above 30 percent, but polls show a majority of the public say he should remain prime minister.

Ishiba faces a tough road ahead with Washington and domestic lawmakers likely to press him for higher public spending and tax cuts at the same time, analysts said.

Experts have voiced worries that Trump, without consulting Asian allies, may make deals with China.

Possible fresh US tariffs on Chinese and Japanese goods may fuel inflation, while the Trump administration may demand Japan to hike its defense spending or push Japanese firms to expand their factories in the United States.

"It must be Mr. Ishiba who is feeling the toughest headache of Mr. Trump's victory," Hideo Kumano, chief economist at Dai-ichi Life Research Institute, wrote in a note.

If Ishiba is nominated prime minister, he will announce a new cabinet on Monday afternoon, who will be officially appointed by the emperor the same day.