Peter Dutton's behalf, then they are cowards working behind the scenes".
Cabinet minister Christopher Pyne said earlier Mr Dutton had told him the prime minister has his absolute support.
The embattled prime minister has faced serious questions over his leadership in the past week amid changes to his National Energy Guarantee policy.
The leadership was declared vacant within minutes of the Liberal MPs gathering in Parliament House for their regular meeting on Tuesday morning, triggering a vote.
Mr Dutton attended Mr Turnbull's office on Tuesday morning, shortly before the prime minister made the leadership announcement. But deep discontent has been brewing for a while, with Turnbull's critics unhappy with him on a range of fronts, and the Coalition losing 38 consecutive Newspolls.
But the bill had support from lawmakers outside Turnbull's center-right Liberal Party, and it appears likely that the leader is caving to pressure from conservative members of his own party, according to the Times.
"I think there might be a second phase strategy here".
"He (the PM) thanked the colleagues for their support".
35 Liberal MPs - a significant chunk - voted for Peter Dutton in a surprise vote Turnbull called.
Sky News is reporting that after Mr Turnbull called the spill, Mr Dutton put his hand up to challenge.
This week Mr Turnbull was hit by former prime minister Tony Abbott for his backflip on plans to legislate the Paris emissions reduction target.
"I'm certain he is telling the truth", he told the Nine Network.
A successful challenge to Turnbull's prime ministership would have been the fifth change in national leadership since 2009, with no prime minister seeing out a full term in office since 2007.
"If we are fighting amongst ourselves, guess what, when the voters go to the election, they'll mark us down as they should", Mr Laundy said.