Former Abbott government minister Eric Abetz has talked down the importance of the Liberals' leadership to the government's success.
Debate has erupted within the Liberals over whether Mr Turnbull will be seeking re-election mainly on the record of his predecessor Tony Abbott.
Mr Abbott says it will be easy for him to campaign for the Turnbull government "because they're running on the Abbott government's record".
The prime minister says that while there has been "continuity" with the previous government, there have also been changes to existing policies or new policies.
Senator Abetz, a staunch supporter of Mr Abbott, said the former prime minister had built "a very good foundation".
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"I have never subscribed to the cult of personality, I subscribe to the ... coalition providing good government for the people of Australia," Senator Abetz told Sky News on Thursday.
"From time to time the prime minister will change, but the fundamental philosophy and fundamental policies remain."
He said Mr Turnbull could look back on "six months of achievement" and set his own legacy beyond the election.
"Who might lead from time to time is of interest, but it's the fundamental underpinnings that are important to me," said Senator Abetz, who was demoted from cabinet after Mr Turnbull took over.
Labor says Mr Turnbull is desperate to make his government look different to that of Mr Abbott, who was ousted in September after polls showed the coalition's stocks in freefall.
Opposition environment spokesman Mark Butler said the latest example of this was the prime minister keeping the Clean Energy Finance Corporation in place, which Mr Abbott wanted to abolish but faced Senate resistance.
