Mr Abbott lost his Sydney seat of 24 years on Saturday night to Zali Steggall, a barrister who was the first skier to win a Winter Olympics medal for Australia.

Speaking with reporters on Sunday, she congratulated Prime Minister Scott Morrison and described her win as "a message from Warringah ... getting away from climate wars".

"Mr Abbott was, I think, very negative when it came to progress on climate change policy and I think now is an opportunity for Mr Morrison to get on with the job," she said.

"The major person who has been against climate change action, I think, is probably Mr Abbott.

"I actually think it is a message from this electorate ... the handbrake is now off."

She said climate change had been an important issue for the electorate for some time and the considerable swing against Mr Abbott at the previous election had "just continued" because constituents wanted action.

Ms Steggall also said the overall election result reflected voter rejection of Labor's economic policy.

Mr Morrison has not yet called to congratulate her.

"I suspect he is waiting to see the outcome of the government," she said.

In conceding defeat, Mr Abbott said it was disappointing to lose his seat but congratulated Ms Steggall while his supporters booed at the mention of her name.

Former PM John Howard said he "grieved" for Mr Abbott's loss and saluted the "enormous contribution that Tony has made to public life in Australia".

Mr Abbott hinted he wasn't done with politics, stating: "My public life will, I imagine, go on".

With more than 78 per cent of the vote counted on Saturday, Ms Steggall had 57.8 per cent of the vote on a two-party preferred basis while Mr Abbott had 42.2 per cent.

Australian Associated Press