Australia’s prime minister Malcolm Turnbull has survived a leadership challenge, defeating a senior minister in an internal government ballot.

His challenger, Home Affairs Minister Peter Dutton, resigned from Cabinet after the vote but the amount of support he gained a day after downplaying the possibility of a challenge surprised many commentators.

Mr Turnbull called the vote at a meeting of conservative Liberal Party politicians as speculation mounted about his support within the government.

Government politician Nola Marino said Mr Turnbull won 48 votes to 35.

Before the ballot, Environment Minister Josh Frydenberg had warned government colleagues that they would lose popularity if they dumped Mr Turnbull.

Mr Frydenberg said voters were tired of governments repeatedly changing their prime ministers.

Ousting Mr Turnbull would be a sixth leadership change in less than 11 years. The centre-left opposition Labour Party elected one leader, Keven Rudd, twice during a chaotic six years in power.

“There is a high transaction cost from changing leaders. Labour’s seen that, we’ve seen that,” Mr Frydenberg told Australian Broadcasting Corp.

“I believe that Malcolm Turnbull is the right person to lead us to the next election.”

Mr Turnbull made a major concession to his opponents within his party on Monday by abandoning plans to legislate to limit greenhouse gas emissions.

The concession avoided the most conservative government politicians voting against the legislation in Parliament, openly undermining his authority.

But former prime minister Tony Abbott, who was replaced by Mr Turnbull in a ballot of government politicians in 2015, was not convinced that Mr Turnbull had given up on reducing Australia’s greenhouse gas emissions by 26% below 2005 levels through legislation.

“What we want to know is: Where are this prime minister’s convictions?” Mr Abbott told the ABC outside Parliament House on Monday night.

“It was a conversion of convenience this morning,” Mr Abbott added.

Damian Drum, a politician in The Nationals’ party, a junior coalition partner, called on Mr Abbott to resign from Parliament instead of destabilising the government.

“He vowed that he wouldn’t be a wrecker,” Mr Drum told reporters of Mr Abbott.

“That’s exactly what he’s been — a wrecker, and he needs to get out of the joint.”

Mr Frydenbeg said Cabinet ministers on Monday night expressed their support for Mr Turnbull, including Mr Dutton, who was a staunch ally of Mr Abbott.

Deputy Liberal Party leader Julie Bishop retained her position unopposed at Tuesday’s ballot.

Australia has gone through an extraordinary period of political instability since prime minister John Howard lost power in 2007 after more than 11 years in office.

Mr Turnbull would next month become Australia’s longest serving prime minister since Mr Howard, having held the office for three years and four days.

The government has trailed Labour in most opinion polls since the last election in 2016. Australians are due to hold a general election early next year.