By Kirsty Needham, Alasdair Pal and Christine Chen

SYDNEY (Reuters) -Australia’s Anthony Albanese claimed a historic second term as prime minister on Saturday in a dramatic comeback against once-resurgent conservatives that was powered by voters' concerns about the influence of U.S. President Donald Trump.

Peter Dutton, leader of the conservative Liberal party, conceded defeat and the loss of his own seat - echoing the fate of Canada's conservatives and their leader whose election losses days earlier were also attributed to a Trump backlash.

Supporters at Labor’s election party in Sydney cheered and hugged each other as Albanese claimed victory and said his party would form a majority government.

"Our government will choose the Australian way, because we are proud of who we are and all that we have built together in this country," Albanese told supporters.

"We do not need to beg or borrow or copy from anywhere else. We do not seek our inspiration from overseas. We find it right here in our values and in our people," he added.

Albanese would be the first Australian prime minister to win a consecutive term in two decades. He said Australians had voted for fairness and "the strength to show courage in adversity and kindness to those in need".

The Australian Electoral Commission website projected Labor would win 81 of 150 seats in the House of Representatives, increasing its majority in parliament, with 68% of the vote counted.

Dutton - whose Liberals had been leading in opinion polls as recently as February until he became dogged with comparisons to Trump - said he had phoned Albanese to congratulate him.

"We didn't do well enough during this campaign. That much is obvious tonight, and I accept full responsibility for that," Dutton said in a televised speech.

The former policeman with a reputation for being tough on crime and immigration said he had spoken to Labor's candidate in the seat of Dickson he had held for two decades, and congratulated her on her success.

"We have been defined by our opponents in this election which is not the true story of who we are" Dutton said, promising the party would rebuild.

TRUMP COMPARISONS

Cost-of-living pressures and concerns about Trump's volatile policies had been among the top issues on voters' minds, opinion polls showed.

"If you sling enough mud it will stick," said Liberal Senator for the Northern Territory Jacinta Price, whose comments that her party would "make Australia great again" had fuelled comparisons to Trump's own "Make America Great Again" slogan.

"You made it all about Trump," she said on ABC. Dutton had said he would appoint Price to a ministry of government efficiency, one of several echoes of Trump's policies.

"Losing Peter Dutton is a huge loss," she added.

Opposition Liberal Party spokesman, Senator James Paterson, defended the conservative campaign, which he said was negatively affected by "the Trump factor".

"It was devastating in Canada for the conservatives ... I think it has been a factor here, just how big a factor will be determined in a few hours' time," he earlier told ABC.

Earlier, as counting got under way, Labor Treasurer Jim Chalmers said the government had been "in all sorts of trouble" at the end of 2024 but got back into the contest because of Albanese's strong campaign performance, policies that addressed concerns about the cost of living, and the Trump effect.

As the results started emerging, he told ABC the projected victory was "a win for the ages”. Albanese "has pulled off one of the great political victories since federation,” he said.

The results were "absolutely unbelievable", Labor supporter Melinda Adderley, 54, said through her tears at the election party.

(Reporting by Kirsty Needham and Alasdair Pal in Sydney; Editing by Edmund Klamann and Andrew Heavens)