Anthony Albanese has held “constructive” talks on trade and security with incoming US president Donald Trump, congratulating the Republican on his election victory.

The prime minister was among the many world leaders who have spoken to Mr Trump following his comeback electoral win, which made him the first president in more than 130 years to claim non-consecutive terms in the White House.

Mr Albanese said the pair discussed trade, security and the AUKUS partnership during their phone conversation.

“As prime minister, I have made it a priority to invest in relationships with world leaders, to build trust and respect in Australia’s best interests,” he told parliament on Thursday.

“I built that with President (Joe) Biden and I will do so with President Trump. 

“The election of a new administration is a new opportunity to emphasise, once again, all that Australia brings to the table.”

Earlier, Mr Albanese said although the federal government expected an approach from the Trump administration that would vary compared to previous presidents, the bond between Australia and the US would be strong.

“President Trump has run a campaign based on change, he’s made it clear that he’s going to do things differently, so we shouldn’t be surprised as things change.

“But equally, we should be really confident in ourselves, our place in the world as well, and our ability to deliver in our interests together as Australians.”

Opposition Leader Peter Dutton also praised the president-elect following the election victory.

“We will make sure that President Trump is not somebody to be scared of, but somebody that we can work very closely with, and that’s exactly what we will do,” he told parliament.

“We want the United States to continue to be the great democracy that it is.”

The prime minister also backed the performance of Australian ambassador to the US Kevin Rudd, despite Dr Rudd’s previous comments criticising Mr Trump.

Social media comments from Dr Rudd have been deleted following the election.

Opposition foreign spokesman Simon Birmingham questioned at Senate estimates why the ambassador had not deleted tweets criticising Mr Trump before he was re-elected president, given Dr Rudd had been a diplomat for some 18 months.

Department officials pointed to Dr Rudd’s statement, saying it was out of respect for the office of president, to which Mr Trump had now been re-elected.

They defended his tenure amid criticisms he would be ineffective under a Trump presidency due to his previous critical statements, noting the passing of key bipartisan legislation in Congress to enable AUKUS during his tenure.

“He has very extensive networks and we have no indication there will be any negative impacts in the United States to this deletion,” deputy secretary Elly Lawson said.

Greens senator Sarah Hanson-Young said women in Australia were anxious about the consequences of Donald Trump’s presidency and whether it meant cutting access to abortion would be on the table at the next Australian federal election.

“Whether it’s women, the planet or democracy, Donald Trump is a threat and Australia can’t just pretend that things haven’t changed,” she said.

“The world has changed this week and we have to rethink what this means for our relationship with the United States.”

Australia could not be in lock-step with the US and “desperately” needed to pull out of AUKUS, Senator Hanson-Young said.

By Andrew Brown and Dominic Giannini in Canberra