Mr Cosgrove is British Queen Elizabeth's representative in Australia and would need to be on hand to swear in a new prime minister if Mr Turnbull was ousted, or to accept Mr Turnbull's request to dissolve Parliament if he decides to call an early election.
Former Home Affairs Minister Peter Dutton needs 43 signatures for Turnbull to call a party room meeting and there are reports that number has quickly climbed over the past 24 hours.
Mr Turnbull won the Tuesday contest only by seven votes. The balloting of party members who are not lawmakers takes a month, meaning Australians will never again wake to news that a Labor prime minister had been changed without warning.
Dutton and his supporters, including former prime minister Tony Abbott who once described climate change as "absolute crap", argue that keeping power prices down was more important than meeting Canberra's commitment to slash carbon emissions by 26 percent by 2030.
On Tuesday Mr Dutton attempted to topple Mr Turnbull, but was unsuccessful.
Last night, the Dutton forces were claiming they had 40 signatures, with many, while supporting the contender, reluctant to sign for fear of repercussions.
"A few minutes ago I spoke with Malcolm Turnbull to advise him I believed the majority of the party room no longer supported his leadership".
Bishop said the resignations of Dutton and Concetta Fierravanti-Wells, the former minister for global development and the Pacific, were accepted.
When questioned if he would ask his supporters to back Treasurer Scott Morrison for the job if a spill was carried, Turnbull refused to answer, but said he would not give in to bullies.
Former minister Peter Dutton has announced his intentions of wanting to stand for election as prime minister.
ADL skewers Trump for tweet on white South African conspiracy theory
Gaspard was a Democratic Party leader when Obama appointed him as the USA ambassador to South Africa. Sisulu said she had instructed officials in her department to meet with the US.
Australian lawmakers told reporters that party rebels were petitioning for another vote as early as Wednesday, though it appeared unlikely that the move would get enough support before Thursday.
"If this occurs, I will still attend National Party meetings if invited".
"Out of respect for my party, I spoke with the deputy PM and my colleagues", he said.
Treasurer Scott Morrison also pledged to challenge for the top job, local media reported.
No Australian prime minister has lasted a full three-year term since John Howard lost power in 2007 after more than 11 years in office.
Another of the moving parts of this leadership crisis was the subject of that first vote: the matter of whether Dutton should be disqualified on the grounds that his family trust has an interest in two childcare centres who benefit from millions of dollars in government subsidies.
The opposition narrowly lost a vote in Parliament that would have sent Dutton to court to determine whether he is eligible to be a prime minister.
"There will be no question time today because they don't know who their ministers are. they don't know who their prime minister is", he thundered across the chamber.
"It was well known to the government and the Opposition, yet they didn't bring it to the Parliament", he said.
Mr Dutton, a hardline conservative who carved out his reputation overseeing Australia's harsh immigration policy, is unpopular with moderate voters, raising the possibility that a third, centrist candidate might still emerge.
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