The disaffected South Australian senator, who will lead the new Australian Conservative party, said he will provide an alternative for conservative voters who have lost faith in the Liberal Party.
Immigration minister Peter Dutton thought that the people would be angry about the defection and the betrayal of the Liberal Party values.
"I appeal to everyone who wants smaller, stronger governments and who wants a freer, fairer country to continue to support the Liberals because that is the only way to improve our party, our government and our country".
'What I have come to the conclusion is that the deterioration of the vote, the lack of faith and confidence in the body politic and in the major parties is not going to stop'.
"We saw a lacklustre campaign, it was bereft of ideas, and people ran away from us at a rate of knots".
Such a result would likely push Bill Shorten's Labor Party ahead of the Coalition on primary votes and make the job of winning government with preferences from The Greens that much easier.
Senator Bernardi says he knew he had to leave the party after the "disastrous" 2016 result.
When asked this morning what advice he had for Senator Bernardi, Mr Joyce said he should "pray, pray hard".
Family First state leader Dennis Hood told InDaily Day had quit that party's executive and he understood he had also handed in his membership, but he believed there was unlikely to be a formal arrangement between the former senator and Bernardi.
Minister for Education Simon Birmingham labelled Bernardi's move a "dog act".
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She says in her Senate career, she has only voted against one nominee in committee, because she says, he wasn't honest with her. Her decision follows intense pressure from her constituents, who have flooded her office with emails, calls and visitors.
Financial Services Minister Kelly O'Dwyer said Senator Bernardi was on an ego trip and should have been "up front and honest" with voters before the last election.
"While Cory and I have sometimes disagreed I'm disappointed that more effort has not been made to keep our party united", he said.
She admitted she now knew very little of Senator Bernardi's positions on agriculture policy or in general, "other than that he's a staunch conservative, supports small government, lower taxes and has more conservative views generally".
He reminded the senator he had been elected as a Liberal by South Australians only seven months ago.
"It really is time for a better way - for a conservative way", he said.
"He's talked about the importance of keeping faith with the electorate".
"We look forward to making sure that we can first of all understand (Senator Bernardi) and what he's about and that he understands us".
Meanwhile, Opposition Senate leader Penny Wong turned her focus to Prime Minister Malcolm Turnbull, calling his "failed leadership" the reason behind Senator Bernardi's move.
As to whether he would be involved in the formulation of public policy with Bernardi, Day said: "We'll see".