Mr Turnbull defeated Home Affairs Minister Peter Dutton in a party room ballot in Canberra on Tuesday.
The PM says he asked Dutton to stay on and keep his ministerial portfolio but that the offer was rejected. Treasurer Scott Morrison would act as interim home affairs minister, Turnbull said.
If just seven more Liberal MPs switched their support to Mr Dutton, he would have the numbers to seize the leadership.
"The problem is that Bill Shorten would be a disastrous prime minister of this country and I believe I had the best prospect of leading the Liberal party to success at the next election".
'If the prime minister's own party don't want him, why on earth should the parliament put up with him?' Mr Shorten said.
Senator Fierravanti-Wells said she pushed for Mr Dutton to replace Julie Bishop as deputy Liberal leader to improve stability.
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Dutton then refused to rule out a second leadership challenge. Turnbull caved in, triggering the leadership ballot.
But with the Turnbull's government at war with itself as a conservative faction has leveraged a slim parliamentary majority to challenge policy it disagrees with, voters may set aside questions over Shorten's leadership.
Again: Turnbull has not yet formally accepted the resignation of anyone except Dutton at this stage. Disquiet with Turnbull had been building for some time, with the government trailing Labor in 38 consecutive opinion polls.
Mr Turnbull's narrow victory leaves him vulnerable to another challenge before the next election.
"We know that disunity undermines the ability of any government to get its job done and unity is absolutely critical", Turnbull added. But he must return to the polls by May next year and could break the impasse by calling an early election.
"I believe strongly that we can win the election if we get the policies and the message right about lowering electricity prices, about making sure that we can do more on infrastructure and in particular around the migration program, until the infrastructure can catch up in our capital cities".
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"It is really important that we put these differences behind us and get on with our job of looking after the 25 million Australians who have put us here", he said afterwards.
He pinpointed former Prime Minister Tony Abbott, who Turnbull ousted in a 2015 party room coup, as a key player behind the move.
His position remains in jeopardy despite surviving Dutton's challenge, stoking expectations of further political instability in a country that has seen six different leaders since 2009.
"I think the public would react very negatively to another change of leadership without them having a vote", he told the Nine Network.
Turnbull addressed media and said Australians don't like it when politicians are "focused on ourselves or talking about each other".
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