Opposition Leader Malcolm Turnbull remains as leader after a vote to call a spill was rejected.
The motion for the spill, moved by Wilson Tuckey, was lost 48 votes to 35.
At the end of a 20-minute meeting, Mr Turnbull thanked his colleagues and urged party unity.
Earlier today, three shadow parliamentary secretaries quit the front bench in protest at Mr Turnbull's decision to support an emissions trading scheme.
The three are Mathias Cormann, Brett Mason and Mitch Fifield. All sent letters to Mr Turnbull this morning.
Mr Cormann was shadow Parliamentary Secretary for Health Administration, Mr Mason was shadow Parliamentary Secretary for Education and Mr Fifield was shadow Parliamentary Secretary for Disabilities, Carers and the Voluntary Sector.
After earlier rejecting calls to hold a ballot, Mr Turnbull decided to try to settle the issue of his leadership.
He was set to be challenged by former Howard government minister Kevin Andrews. Frontbenchers Joe Hockey and Tony Abbott did not stand.
Mr Andrews based his tilt for the top job on the fact that many in the party are unhappy with Mr Turnbull’s decision to push through support for an emissions trading deal.
"For these reasons I will put my hand up if there is a successful motion to have a spill this afternoon,’’ he said this morning.
‘‘A majority of my colleagues in the party room yesterday were of the view that either this legislation should be rejected or that it should at least be delayed until we know what the rest of the world is doing in terms of the meeting in Copenhagen,’’ he said.
Mr Andrews said he was concerned about the direction the Liberal Party was taking under Mr Turnbull.
‘‘What’s important for the leader of the Liberal Party at this stage is to make sure that he or she takes his or her colleagues with them. It’s important that we are united,’’ he said.
‘‘You all know that old saying of Bob Hawke. I think it was that if you can’t govern yourselves, you can’t govern the country.’’
Mr Andrews said he was ‘‘quite sceptical’’ about the impact of man-made emissions on global warming.
‘‘I think that climate change is occurring [but] the jury is out on what to any extent human beings are involved in it,’’ he said.
Recent revelations overseas showed what appeared to be ‘‘quite deliberate manipulation’’ of data.
Computer hackers have broken into a server at a well-respected climate change research centre in Britain and posted hundreds of private emails and documents online.
The decades worth of correspondence has stoked debate over whether some scientists have overstated the case for man-made climate change.