The Victorian premier, Jacinta Allan, has thrown down the gauntlet to Labor powerbrokers, vowing to fight any attempt to oust her as leader amid a push for her to stand down before parliament resumes this week.

Just four months before a state election, factional conveners from Labor’s left and right met on Sunday night to discuss whether Allan still had the support of a majority of the caucus. It is understood that the group agreed she did not.

Several Labor sources have confirmed a cross-factional group of ministers met Allan before Monday’s scheduled cabinet meeting to tell her they believed she has lost the majority of support and urged her to stand down.

The group included MPs from the premier’s own socialist left faction, including ministers Ingrid Stitt and Gabrielle Williams, and MP Mathew Hilakari, as well as right-aligned frontbenchers Anthony Carbines and Lizzie Blandthorn.

It was their hope that she would step down before a potential leadership vote at Tuesday’s caucus meeting, the first sitting day of parliament after the winter break.

If Allan steps down, it will allow her most likely opponent – the deputy premier, Ben Carroll – to run unopposed for the leadership.

But in a letter to the Victorian Labor state secretary, Steve Staikos, Allan indicated she will contest a leadership ballot – which would trigger a weeks-long process where both the parliamentary caucus and rank-and-file Labor members will vote.

The process, introduced after the instability of the Rudd-Gillard-Rudd era, is untested, but would see a leader elected based off 50% of MPs votes and 50% party members.

“I refer to media speculation regarding the leadership of the Victorian Parliamentary Labor Party and am writing to request that you ensure that the Victorian Labor Party is prepared to conduct an election for the leadership of the State Parliamentary Labor Party in the event an election is required,” Allan says in the letter, seen by Guardian Australia.

“As you are aware the Victorian Labor Party rules require State Secretary to provide administrative support to ensure the effective conduct of a ballot of all eligible party members.

“I would also like to formally notify you of my intention to be a candidate for the leadership of the Victorian Parliamentary Labor Party in the event that an election is required.”

A party spokesperson said no public comments would be made on the matter “at this time”.

The letter bolsters claims by ministers close to Allan that she would fight a possible challenge.

One minister told Guardian Australia that Allan was “not going anywhere” and described the leaking of the meeting as an attempt to build momentum for a spill.

Another said not all parliamentarians within the left faction were consulted before the meeting and that there was “no uniform position” within the grouping.

“There is no vacancy, no challenger and no consolidated position within the left,” the minister said. “It’s just one big smoke machine.”

The attorney general, Sonya Kilkenny, a key supporter of the premier, said leadership speculation was “idle gossip” on Sunday.

“She has my full support, and this idle gossip doesn’t help Victorians,” Kilkenny said. “It is only hurting Victorians at a time when Victorians need us all to be focused on them, and that is exactly what Jacinta Allan and our Labor government, our team, is doing.”

Allan became premier after the resignation of Daniel Andrews in September 2023.

Momentum had been building for a leadership spill before parliament rose for a winter break in June due to poor polling and Allan’s weak personal approval ratings, rising support for One Nation and concerns about her response to organised crime infiltrating the state’s Big Build, via the construction union.

Allan, who previously served as the minister for transport infrastructure overseeing the Big Build, has rejected growing calls for a royal commission.

But Carroll ruled out a challenge at the time, at an awkward press conference where he looked Allan in the eye and declared he would not challenge her for the leadership.

At the same 15 June press conference, he told reporters: “I’ve got a young daughter at home, and I couldn’t be more proud to make sure she grows up knowing that I supported Jacinta Allan to be a world-class premier and get re-elected in her own right.”

It is understood Carroll, if elected leader, would immediately call for a royal commission, work to resolve the pay dispute between the state government and public school teachers, and attempt to improve the party’s economic credentials and standing with the business community.