The government has trailed the centre-left opposition Labor Party in most opinion polls since the last election in 2016.
Speaking outside of Parliament House in Canberra, following the vote, Turnbull urged his colleagues to show "unity".
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.
The longer Mr. Turnbull remains prime minister, the worse the government's opinion polling was likely to become, Mr. Economou said.
After the leadership spill, the parliamentary theatre comes.
"If the prime minister's own party does not want him, and almost half of his party voted against him remaining prime minister, why should the parliament put up with him?" Australians are due to hold a general election early next year.
Malcolm Turnbull may have claimed victory in Peter Dutton's leadership challenge, but could face another contest within weeks, with nearly half of his MPs wanting him gone.
"Having lost the ballot today, my job is to respect the view of the party room which I do", he said. He refused to say, but added: "I have gone through what my job is now and that is to make sure that I can help the Coalition win the next election".
"We've seen it so often in Australian politics - this two-stage act play in removing a prime minister - and, given how close the vote was, there's definitely more to come", said Haydon Manning, a political science professor at Flinders University in South Australia state.
The prime minister caved in to their demands to remove emissions reduction targets from the legislation, but it still wasn't enough.
But that was hardly the resounding vote of confidence Turnbull sought.
Even if Malcolm Turnbull survives a second challenge against Peter Dutton, he looks set to lose the election in a landslide to Labor's Bill Shorten, following 38 consecutive Newspoll losses with this challenge denting his already-crumbling authority.
With 35 votes to Malcolm Turnbull's 48, Dutton only needed another 7 MPs to support him in order to oust the prime minister.
But it's understood Mr Turnbull is not accepting the resignations of a number of other ministers, including Cybersecurity Minister Angus Taylor, Assistant Treasurer Michael Sukkar and Assistant Minister to the Prime Minister James McGrath. He won that vote, as he did on Tuesday, 48-35. That resignation was quickly followed by Senator James McGrath, Concetta Fierravanti-Wells and then up and coming Law Enforcement and Cyber Security Minister Angus Taylor.
"Our conservative base strongly feel that their voice has been eroded", she wrote to Mr Turnbull.