The prime minister said he had a "warm and productive" call with the US president on Thursday night.
Mr Albanese said he reiterated calls for the US to drop its 12.5 per cent tariffs on Australia, which came into effect in July.
"I put the case as strongly as I could. It was a constructive discussion about why Australia should get at least the best treatment," he told reporters in Canberra on Friday.
"I did ask that Australia's position as a friend of the United States be considered, and the president agreed that he would give consideration to my request."
Australian exports previously faced a baseline 10 per cent tariff under US trade policy before being increased to 12.5 per cent, with the US government citing concerns over modern slavery laws.
Australia has called for their removal, given a US trade surplus.
"I informed him about our record when it comes to dealing with issues such as modern slavery, the strengthening that we have put forward as well, to look and hold companies accountable for the supply-chain process as well," Mr Albanese said.
"We have a different view, a different perspective.
"What I was able to do was to put the case to the president not in ideological terms, because the position is what it is."
The two leaders also discussed the AUKUS submarine deal, the US war on Iran and Australia's recent alliances in the Pacific.
"We agreed it (AUKUS) was a project that is and will continue to deliver benefits for the United States, for Australia, and for the United Kingdom," Mr Albanese said.Â
The pair discussed the second pillar of the program, which includes enabling systems for uncrewed undersea vehicles.
The call came hours after Pentagon official and former AUKUS sceptic Elbridge Colby confirmed to journalists the mega-deal was "full steam ahead".
Mr Colby, who is the US under secretary of war, originally wrote what was perceived to be a sceptical review of the submarine deal before revising it to be more in line with Mr Trump's view.
The Pentagon recently admitted construction of US Virginia-class nuclear submarines was languishing at about 1.1 to 1.2 boats annually despite needing 2.33 boats a year to meet AUKUS requirements.
Foreign Minister Penny Wong told the Lowy Institute on Friday the submarine deal remained crucial for Australia.
"We have a capability issue we had to address, which is we had a submarine capability which needed to be replaced," she said.
"The US remains so critical to us and to the world."
Mr Albanese said the phone call included an extensive update on the situation in the Middle East.
"We did continue to say that Iran shouldn't be allowed to have nuclear weapons," he said.
Mr Albanese briefed the US president about a Chinese ballistic missile test in the Pacific in July, which has been condemned by leaders in the region.
"This caused a great deal of concern right across the Pacific, which is true," Mr Albanese said.
He has spoken with Mr Trump at least five times since becoming prime minister. They have also met in person.
Mr Albanese is set to meet with Mr Trump later in the year, with a trip to the United Nations in September and travel to the G20 summit in Florida in December on the cards.
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