Those who offered their resignations had all backed former Home Affairs Minister Peter Dutton in the leadership challenge, which was narrowly defeated.
The challenge was for the leadership of the centre-right Liberal Party, the dominant partner in the coalition government.
Foreign Minister Julie Bishop told ABC: “A number of people who voted for Peter Dutton have in fact offered their resignations to the Prime Minister.
“They’ve done the right thing, but the Prime Minister has said that he wants them to remain in the ministry.”
Those who were asked to remain in post included Trade Minister Steven Ciobo and Health Minister Greg Hunt, two of Mr Turnbull’s top critics.
However the resignations of Mr Dutton and Concetta Fierravanti-Wells, former Minister for International Development and the Pacific, were accepted.
Mr Turnbull survived the leadership contest by only 48 votes to 35.
However the narrow margin means he could face a second contest, especially as Mr Dutton is now out of the Cabinet.
Mr Turnbull, a social liberal, has had a poor relationship with the more conservative wing of his party.
Earlier this week, under right-wing pressure, he was forced to weaken the government’s centrepiece environmental proposal.
The policy would have forced the country to cut its carbon emissions by 26 percent by 2030 compared to its 2005 levels, as was agreed under the Paris Agreement.
However, this proposal was watered down by conservative lawmakers, who argued it would cost jobs and cut economic growth.
Former Australian Prime Minister Tony Abbott, who signed up to the Paris Agreement in 2015, now thinks his country should quit.
He argues this is the only way to end “the emissions obsession that’s at the heart of our power crisis”.
In June 2017 President Donald Trump also controversially withdrew the US from the Paris Agreement.