Mr Trump has flagged a lift in global tariffs to 15 per cent, after the country's Supreme Court found existing measures for a 10 per cent tariff unlawful.
The president said a different power would be used to implement the tariff, which will kick in from Tuesday.
Senator Farrell said he would travel to the US for talks with American officials, raising the case for the economic measures to be removed.
"We have got a free trade agreement with the United States. That free trade agreement provides that we have tariff-free access for our products into the United States," he told reporters in Canberra on Monday.
"The message I'll be giving to the Americans over the next few days is we expect you to honour that agreement."Australia previously had a 10 per cent tariff on exports to the US, the baseline rate imposed by the US.
Steel and aluminium imports carried a 50 per cent tariff.
Trade experts have warned the advantage enjoyed by Australian exporters compared to other countries due to the lower tariff rate could be eroded if the 15 per cent rate comes into effect.
Despite the hike on tariffs, an exemption on Australian beef is expected to remain in effect.
"Our argument is the correct argument. We believe in free and fair trade," Senator Farrell said.
Opposition trade spokesman Kevin Hogan said the US needed to honour its obligations.
"The strength of our economic partnership has been built on trust and mutual benefit. Any deviation from this agreement undermines the principles of free trade and the rules-based order," he said in a statement.
"Unilateral tariff hikes undermine confidence and disrupt global supply chains. They also increase the risk of retaliation and economic instability."
Senator Farrell said the trade situation with the US had reinforced the need to land other trade deals, with a long-awaited agreement with the EU close to being finalised.
"There's now greater impetus, both on our part and on the part of the Europeans, to get a free trade agreement," he said.
"This is an agreement involving 450 million Europeans, an economy of $30 trillion, we're determined to get an agreement with them."
Further talks are expected on the EU deal once the minister returns from the US.
