New Liberal federal president Tony Abbott has sought to rally the party at “this time of existential crisis”, labelling it “the patriot party” and declaring it must boost its membership.

While not directly mentioning the threat from Pauline Hanson, One Nation’s surge was clearly in Abbott’s mind when he addressed the Liberal federal council in Melbourne after being elected president unopposed on Friday.

“My fellow Liberals, our challenge is to persuade the sceptical public that we remain the most credible alternative party of government in this country,” he said.

Abbott said he owed the Liberal party “big time”. “That’s why I regard it as my duty to serve the party in this time of existential crisis.”

The council meeting comes as the party has been encouraged by the backlash against the budget, with the government having a fight on its hands over its capital gains tax changes, and being forced to look to some carve outs.

But more generally, the Liberals are fearful of the dramatic rise in One Nation support and the plunge in Coalition numbers, with a recent poll suggesting it would be nearly wiped from parliament in an election held now.

Among Liberals there are mixed feelings about the Abbott presidency, with some saying he will bring enormous energy to the job and others worried he will overshadow opposition leader Angus Taylor.

Abbott said that as the last successful Liberal federal leader of the opposition “I do believe I have the ability to help Angus Taylor to be the next successful federal leader of the opposition and to become our 32nd prime minister”.

He praised Taylor for policy leadership but said he had to be backed by a strong organisation.

That meant, “first and foremost”, increasing party membership. Even on the most optimistic figures, Abbott said, the party only had 50,000 members – the same as 30-40 years ago when the population was scarcely half its present number.

The Conservative party in Canada had 400,000 members. “On a per capita basis we would have at least 250,000 members.”

“And that’s what we need to do, to mobilise the good people of Australia in a good cause – the cause of better government based on our values.

“We are the freedom party, the tradition party, but above all else we are the patriot party, which is why, at our best, we should be absolutely unbeatable.”

The Guardian reported on Friday that Abbott was stepping down from his advisory role to the right wing advocacy group Advance, on becoming Liberal president.

Former foreign minister Alexander Downer won one of the vice-president positions.

Taylor, addressing the council on Saturday, will heavily target the integrity of Prime Minister Anthony Albanese in a personal attack.

He will denounce Albanese as the prime minister whose “word is never his bond”, turning the PM’s own word-is-my-bond description of himself back on him.

In his address, released ahead of delivery, Taylor describes Albanese’s pre-election ruling out of changes to negative gearing and capital gains tax as “the mother of all lies”.

“No Australian can trust another word that comes out of this bloke’s mouth,” Taylor says.

He says Albanese doesn’t want to “empower people” but wants “power over people, often saying he wants Labor to be “the natural party of government”.

“That statement is as entitled as it is illiberal. For Anthony Albanese, political life has always been about entrenching Labor rule. His main interest is to consolidate and centralise power.”

Taylor also labels Albanese “unashamedly socialist”. “We must fight and defeat Labor’s socialist vision if we’re going to restore our standard of living and protect our way of life,” he says

Many Australians “feel like second class citizens under Labor,” he says.

“Many of these Australians – who have never been political – are speaking up for the first time.

“We will never have a better opportunity than this. To rally people to our cause To encourage Australians to join us in the fight against Labor by joining the Liberal Party.”