One of Donald Trump's top trade advisers says no country will be granted an exemption from the US President's newly announced tariffs on steel and aluminium, fuelling pessimism inside the Turnbull government about whether Australia's lobbying efforts will secure such an exception.

Peter Navarro, director of the White House's National Trade Council, said the 25 per cent levy on steel and 10 per cent levy on aluminium could be in place this week and, while there was scope for individual businesses to receive exemptions, the measures would apply to all countries.

"There's a difference between exemptions and country exclusions. There will be an exemption procedure for particular cases where we need to have exemptions so that business can move forward but at this point in time, there will be no country exclusions," Mr Navarro told CNN on Sunday night, AEDT.

Donald Trump and Malcolm Turnbull during bilateral meetings in February. Credit:Alex Ellinghausen

However, in a sign of the uncertainty surrounding the President's decision making, US Secretary of Commerce Wilbur Ross said "we shall see" when asked if there would be any exceptions, leaving wriggle room for Mr Trump to change his mind.