The two leaders discussed the election outcome as well as tariffs imposed by the US on allies including Australia, over the phone on Monday.
"I had a very warm and positive conversation with President Trump," Mr Albanese told reporters in Canberra.
"I thanked him for his very warm message of congratulations. We talked about AUKUS and tariffs and we'll continue to engage.
"We will engage with each other on a face-to-face basis at some time in the future ... and I thank him for reaching out in such a positive way.
"He was fully aware of the (election) outcome, and he expressed the desire to continue to work with me in the future."
It was the third time the leaders have spoken, and the first since tariffs of 10 per cent were imposed on all Australian exports to the US.
The two leaders will come face-to-face at the upcoming G7 meeting in Canada, after Mr Albanese was invited to the summit by newly elected Canadian prime minister Mark Carney.
The phone call comes as Mr Trump praised Mr Albanese after Labor's landslide election win, with the US leader not addressing suggestions his presidency contributed to a drop in coalition support.
Speaking to the media at the White House on Monday, Australian time, Mr Trump said he had a good relationship with Australia's re-elected leader.
"Albanese, I'm very friendly with. I don't know anything about the election other than the man that won, he's very good," the president said.
"I can only say that he's been very, very nice to me, very respectful to me.
"I have no idea who the other person is that ran against him, and you know (Albanese and I) have had a very good relationship."
Mr Trump did not respond to questions on whether his policies had caused a rethink from voters in Australia on support for the coalition.
At different points of the campaign, Peter Dutton sought to distance himself from Mr Trump's agenda.
But the coalition was criticised for attacking the public service and taking inspiration from Mr Trump's 'department of government efficiency'.
Mr Trump's policies were a key factor in the recent election in Canada, which returned its centre-left government and punished the right-wing opposition, with its leader losing his seat.
Mr Albanese and Mr Dutton had campaigned on who would be best placed to deal with the Trump White House, following the president's imposition of tariffs on US allies.
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