ACT Liberal Senator Zed Seselja says he believes Peter Dutton would help the government connect better with average Australians if he was made prime minister.
Senator Seselja is backing Mr Dutton to take the top job, having voted for the former immigration minister in Tuesday's Liberal Party leadership spill, won 48-35 by Prime Minister Malcolm Turnbull.
A second spill appears likely on Friday, with Mr Turnbull pledging to call a party room meeting at 12pm if he is presented with a petition showing majority support within the party for a change of leadership.
The prime minister said he would not contest a leadership ballot if that occurred, with Mr Dutton, Julie Bishop and Scott Morrison to stand in the event of a spill.
Senator Seselja, who formally resigned his position as assistant minister for science, jobs and innovation on Thursday, said he would again support Mr Dutton, but refused to say Mr Turnbull was out of touch.
He said he had declined Mr Turnbull's offer to stay in the ministry because he could not give the prime minister a commitment to vote for him in any future leadership contests.
"I think he can connect with people in large parts of Australia," Senator Seselja said of Mr Dutton, predicting that the former Queensland police officer would attract criticism from some quarters because of a perception he was not as visionary as some past prime ministers.
"I'm not going to get into a detailed critique and I'm not in the business of criticising my colleagues, but in the last few years under this government we have started to see some of the support of our traditional supporters erode.
"You can't win an election without your base. It's a called a base for a reason and you build on it with other parts of the community, but you need to listen to your traditional supporters."
Senator Seselja said conservative voters were increasingly deserting the Coalition, a situation brought on by the government's indecisiveness on energy policy and its Catholic and independent schools funding model, which Senator Seselja criticised last year.
"What happened in the Longman byelection is one example [of the drop in support]," Senator Seselja said.
He said the Coalition's prospects at the next election were "a matter for the Australian people", and while he was clear on his support for Mr Dutton as Liberal leader, he called fellow leadership contenders Scott Morrison and Julie Bishop "strong performers".
Senator Seselja denied playing a part in bringing about disunity in the party ahead of Tuesday's spill, which he described as "a shock to everyone".
He said while he had heard "chatter" that Mr Dutton was considering a challenge, he had not had time to talk to the former immigration minister before voting for him and offering Mr Turnbull his resignation.
"There was no time," Senator Seselja said.
"It was just brought on."