Two senior Tasmanian ministers have the weekend to rally the numbers ahead of a partyroom vote on Monday which will determine the state's next premier.
Treasurer Peter Gutwein and State Growth Minister Michael Ferguson are vying for the Liberal leadership after Will Hodgman's sudden resignation earlier this week.
The showdown is seen as a battle between the party's moderate and more conservative factions.
But Mr Hodgman, who stunned many by stepping down after six years in the top job, has downplayed suggestions of a damaging party split and said a contest of ideas isn't a bad thing.
"I don't think it hurts for there to be some competition and a contest for what's a really important job," he told reporters on Friday.
"There's a passion, commitment and drive, right across our government."
Mr Hodgman has confirmed he won't have an official say on who replaces him, even if there is seven-all tie between the 14 voting party members.
"I won't be voting because I think it would be inappropriate for somebody who's not going to be a member of the new team moving forward to make decisions about who the next leader will be," he said.
Mr Gutwein, who is running alongside current deputy premier Jeremy Rockliff, is seen as representing the moderate side of the party.
The more conservative and devoutly Christian Mr Ferguson has predominantly managed the state's troubled health system since the Liberal's 2014 election win but was stripped of the portfolio last year.
Mr Hodgman hasn't publicly endorsed a successor.
"I think we've been a really well-balanced government. Of course in any politic party there are differing views but we've always come together," he said.
At a press conference alongside Mr Hodgman on Friday, MPs John Tucker and Jane Howlett refused to say who they were supporting.
Mr Hodgman will formally step down once a new leader is appointed having spent 18 years in politics.
He said the mid-term exit was the right time for new leadership before the next state poll in 2022.
Australian Associated Press