Tariffs on most Australian exports will remain at a baseline 10 per cent rate despite the US hiking levies on other nations.
Trade Minister Don Farrell said the US president had resisted calls from some within his ranks to increase Australia's rate to 15 or 20 per cent.
"We don't want to leave the issue here," he told reporters in Adelaide on Friday, adding the US should remove all tariffs on Australian products in accordance with the free trade agreement.
"This is a vindication of our cool and calm negotiations with our trading partners. At no stage did we introduce tariffs on American goods."
The trade minister indicated he had invited his US counterpart Howard Lutnick to Australia to continue trade talks.
No US trading partner has managed to totally dodge the tariffs, and the 10 per cent rate is the lowest most can hope for.
The Trump administration released details of country-specific tariff rates for dozens of nations, hours before passing its self-imposed August 1 deadline.
New Zealand goods will be subject to a greater 15 per cent tariff, as will exports from Fiji and Papua New Guinea.
More punitive rates have been imposed on products from several major US trading partners including Canada and India, with the new tariffs due to come into effect on August 7.
Opposition trade spokesman Kevin Hogan said Prime Minister Anthony Albanese still needed to hold one-on-one talks with the US president to secure a better deal and push for the removal of steel and aluminium tariffs.
"We need our prime minister to prioritise the relationship with the US president, not just for economic purposes, but also for national security purposes," he said.
"It doesn't vindicate the Albanese government. (The tariff rate) is based on a formula in the sense that the US have a trade surplus with us."
The government had dodged a bullet but needed to taker a stronger stance against a "dangerous, erratic regime in Washington", Greens senator David Shoebridge said.
"We really need to ensure that our government is not being cowed and bullied and silenced in our behaviour as an international player ... because we're fearful of the next sporadic move by Donald Trump," he told reporters.
In a statement, the White House said tariffs were increased on nations that failed to engage in negotiations with the US or take adequate steps to "align sufficiently on economic and national security matters".
The Albanese government recently wound back biosecurity restrictions on US beef imports, although ministers insist the move was a coincidence and not in response to the tariffs.
The US had complained to Australia about non-tariff trade barriers including longstanding restrictions on beef following a prior outbreak of mad cow disease, and their removal was hailed by Mr Trump as a victory.
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