CANBERRA, Australia — Australia's beleaguered prime minister was resisting pressure to quit as opponents from within his party struggled on Thursday to show that he had lost the government's support.

Prime Minister Malcolm Turnbull demanded the names of lawmakers in the conservative Liberal Party who wanted him to go before he would allow them to choose a new prime minister at a meeting at Parliament House on Friday. The names would provide proof that a majority of his government had abandoned him.

Turnbull would then become the fourth prime minister to be dumped by his or her own party before serving a full three-year term in an extraordinary era of political instability that began in 2010. The trend is universally hated by Australians.

Turnbull's main rival in his government, former Cabinet minister Peter Dutton, has told the prime minister that a majority of Liberal Party lawmakers — at least 43 — don't support his leadership. But Dutton's supporters on Thursday could not find 43 lawmakers prepared to sign their names to a petition demanding a leadership ballot.

An explanation could be that some lawmakers fear they will be punished by voters if they put their names to dumping Turnbull. The ballot to choose a prime minister is secret, so lawmakers don't have to declare which candidate they voted for. Many later lie that they backed the winner.

Support for ousting Turnbull might also have waned because he warned on Thursday he would quit politics rather than ask his party again for its support in a ballot. His resignation from Parliament would force a by-election that could cost the government its single-seat majority. The resignation could also push his successor into immediately calling general elections.

Zed Seselja, a Dutton supporter who has resigned as a Turnbull government minister, estimated 40 had signed the petition by late Thursday. Turnbull should allow the meeting to proceed on Friday without the names of his opponents, Seselja said.

Turnbull insisted that the names of those who wanted him gone needed to be made public.

"These are momentous times and it's important that people are accountable for what they're doing," he told reporters.

Turnbull had defeated Dutton 48-35 in a surprise vote on Tuesday. Turnbull initiated the ballot in the hope of ending speculation that his government had lost faith in him in the face of poor opinion polling. Several ministers have since resigned and told him that most of the government wanted a new leader.

In addition to Dutton, media reports said other lawmakers were considering running for Turnbull's job, including Treasurer Scott Morrison and Foreign Minister Julie Bishop.

Opposition lawmakers reacted with outrage when the government shut down Parliament hours early so that Liberal Party lawmakers could focus on their leadership crisis.

Opposition Labor Party leader Bill Shorten told Parliament it was evidence that "Australia no longer has a functioning government."

"The Liberal Party, whatever it does today and tomorrow, is irreparably split," Shorten said.

His deputy, Tanya Plibersek, told Parliament that whoever emerged as prime minister should immediately call an election — an outcome that some analysts argue is probable. But with the next election due by May, the ruling coalition is far less prepared for an election now than center-left Labor is. The coalition has yet to select many candidates.

The opposition narrowly lost a vote in Parliament that would have sent Dutton to court to determine whether he is eligible to be prime minister. The vote to refer Dutton to the High Court was defeated 69-68 in the House of Representatives before it adjourned.

Dutton has released legal advice that his family's ownership of two child-care centers that received federal funding does not breach a constitutional ban on lawmakers having a pecuniary interest in an agreement with the public service. Some constitutional lawyers say there are areas of doubt.

Such a pending court case could scare lawmakers away from supporting Dutton in a leadership ballot. Government lawyers are investigating his case to see if there are issues for the High Court to determine.

Turnbull said he wanted the government's legal advice on Dutton's eligibility presented to Friday's meeting.