The prime minister won the leadership ballot 48 votes to 35, leading Mr Dutton to resign from his position as Home Affairs Minister on Tuesday.

A group of ministers who voted for Mr Dutton have also offered their resignations to the prime minister, but it's understood Mr Turnbull is not accepting them.

Instead, he's hoping to heal the wounds and move on, similar to how ministers who offered to resign when he took over from Tony Abbott stayed on in 2015.

International Development Minister Concetta Fierravanti-Wells offered her resignation with a letter where she criticised the Liberal Party for moving too far to the left.

"Our conservative base strongly feel that their voice has been eroded," she wrote to Mr Turnbull.

"They needed some demonstrable indication that there are conservative voices around your cabinet table."

Senator Fierravanti-Wells said she pushed for Mr Dutton to replace Julie Bishop as deputy Liberal leader to improve stability.

Assistant Treasurer Michael Sukkar offered his resignation after voting for Mr Dutton in the spill, along with Assistant Minister to the Prime Minister James McGrath.

"I voted for Peter Dutton for Leader of the Parliamentary Liberal Party. As a matter of integrity, this afternoon I offered my resignation to the Prime Minister," Senator McGrath posted on Facebook on Tuesday afternoon.

Senator McGrath was one of the key backers behind Mr Turnbull's rolling of Tony Abbott in 2015.

Cybersecurity Minister Angus Taylor and Human Services Minister Michael Keenan have also reportedly offered their resignations.

Australian Associated Press