The proclamations signed by Trump in this regard a day earlier gives exemptions to only two countries - Canada and Mexico.
However, Trump indicated that the Australian could be the third country. He said he spoke to Australian Prime Minister Malcolm Turnbull in this regard.
"He is committed to having a very fair and reciprocal military and trade relationship. Working very quickly on a security agreement so we don't have to impose steel or aluminum tariffs on our ally, the great nation of Australia!" Trump said in his tweet.
"Thank you for confirming new tariffs won't have to be imposed on Australian steel & aluminium - good for jobs in Australia and in US!" said the Australian premier as he retweeted the US president's tweet.
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Trump had praised Australia during his Cabinet meeting on Thursday.
We have a very close relationship with Australia. We have a trade surplus with Australia. A great country, a country long term partner will be doing something with them. We'll be doing something with some other countries, he said.
White House Press Secretary Sarah Sanders told reporters that in the president's proclamation two countries are specifically excluded.
"There would be the opportunity for us to negotiate on matters of national security with other countries. And we're going to be doing that with a number of different countries," she said.
On Thursday, Trump had said that America will remain open to modifying or removing the tariffs for individual nations.
US Trade Representative (USTR) Robert E Lighthizer has been put in charge of negotiating with countries that seek an alternative to the steel and aluminium tariffs, he said.
The White House said Trump welcomes any country with which "we have a security relationship" to discuss alternative ways to address US concerns, including those about global excess capacity.
He has left open an avenue for potentially modifying or removing a tariff under certain conditions for individual countries, it said.
"Modification or removal of the tariffs would be possible if alternative means are agreed upon to ensure imports from a country no longer threaten to impair our national security. Under the direction of the president, the USTR is responsible for negotiations with countries that seek an alternative means to the steel and aluminium tariffs," the White House said.
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