Senator Seselja offered Mr Turnbull his resignation as assistant minister for science, jobs and innovation after backing Peter Dutton in Tuesday's leadership spill, won 48-35 by Mr Turnbull.

The prime minister did not initially accept Senator Seselja's offer, but with Mr Dutton planning a second strike against Mr Turnbull, Senator Seselja formally resigned on Thursday morning.

A spokeswoman for Senator Seselja confirmed Mr Turnbull had accepted the resignation.

Senator Seselja has been joined in resigning his position by several ministers, including Mathias Cormann, Michaelia Cash, Greg Hunt, Michael Keenan and Mitch Fifield.

Fairfax Media understands Senator Seselja, a staunch conservative in the Liberal Party, voted for Mr Dutton on Tuesday believing he was best able to speak to conservative voters lost since the last leadership change in 2015, and bring them back to the Coalition.

In his resignation letter, Senator Seselja says he was unable to give Mr Turnbull a commitment that he would support the prime minsiter in future leadership ballots.

On Thursday, Mr Dutton said he had spoken to Mr Turnbull and asked him to convene a party room meeting at which he would again challenge for the leadership.

Mr Dutton said he had advised Mr Turnbull that he believed the majority of the party room no longer supported the prime minister's leadership.

Mr Turnbull addressed the media early on Thursday afternoon and said he would call a party room meeting at 12pm on Friday if he was presented with a petition showing majority support for a change of leadership.

He said he would not contest a leadership ballot if that occurred, and reiterated his previous statement that "former prime ministers are best out of the Parliament".

Scott Morrison and Julie Bishop have also entered the race as alternative prime ministers.