The US president has flagged further trade measures, putting more pressure on the federal government after Australia failed to secure an exemption from his 25 per cent tariffs on steel and aluminium.
Greens leader Adam Bandt does not believe retaliatory tariffs would be the right response, but warned the nation should not be "hitching Australia's wagon" to Mr Trump.
"Donald Trump is a threat to peace, a threat to democracy and he's a threat to Australia as well," Mr Bandt told ABC's Insiders program on Sunday.
"Donald Trump right now is attacking marginalised communities at home and delivering for billionaires and he's attacking allies and ripping up longstanding agreements.
"This should be a wake-up call for Australia that we need to rethink our relationship with the United States."
Australia is continuing to negotiate, with Trade Minister Don Farrell having spoken to US Commerce Secretary Howard Lutnick on Friday, but Australia's future remains unclear.
"It wasn't a pessimistic conversation," Senator Farrell told Sky News.
"But he gave no assurances about what might happen in the next round of negotiations."
The trade minister has another talk scheduled with US trade representative Jamieson Greer on Tuesday.
"We're going to work out, firstly, what it is that the Americans want out of this arrangement," Senator Farrell said.
"It's still still not clear to me what it is that they are seeking, but once we find that out, we'll work through this issue, and we'll work through it in Australia's national interest."
The coalition has argued the government should have gone further and sent Prime Minister Anthony Albanese to Washington DC for face-to-face talks with the president.
"This is a Team Australia moment, but where was the captain of the team? He wasn't there," Deputy Opposition Leader Sussan Ley told Sky News.
Mr Bandt wants Australia to move beyond its US relationship towards other countries impacted by tariffs.
"In terms of a lasting arrangement for the future, it has to be based on what's in Australia's interests, rather than hoping Donald Trump will ride to the rescue or somehow give special treatment," he said.
Senator Farrell confirmed Australia had reached out to other nations, such as South Korea, about expanding and diversifying trade relationships.
Mr Bandt also urged Australia to pull out of the AUKUS nuclear submarine agreement with the US, but Labor and coalition politicians insist the deal is in Australian interests.
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