In a statement on Monday, the White House said the details of the deals with Brazil, Argentina and Australia would be finalised shortly and it did not disclose terms.
"The administration is also extending negotiations with Canada, Mexico, and the European Union for a final 30 days. In all of these negotiations, the administration is focused on quotas that will restrain imports, prevent trans-shipment, and protect the national security," the White House said.
A source familiar with the decision said there would be no further extensions beyond June 1 to stave off tariffs.
Trump on March 23 imposed a 25 per cent tariff on steel imports and a 10 per cent tariff on aluminium in March but granted temporary exemptions to Canada, Mexico, Brazil, the EU, Australia and Argentina.
He also has granted a permanent exemption on steel tariffs to South Korea.
Trump has invoked a 1962 trade law to erect protections for US steel and aluminium producers on national security grounds amid a worldwide glut of both metals that is largely blamed on excess production in China.
The tariffs have increased frictions with US trading partners worldwide and have prompted several challenges before the World Trade Organisation.
Trump administration officials have said that in lieu of tariffs, steel- and aluminium-exporting countries would have to agree to quotas designed to achieve similar protections for US producers.
The terms agreed by Brazil, Argentina and Australia to escape the US tariffs were unclear.
South Korea earned its permanent exemption from steel tariffs by agreeing to quotas that will cut its steel shipments by about 30 per cent from 2017 levels.
Seoul is still subject to US aluminium tariffs.
The White House said the agreements reflected administration efforts "to reach fair outcomes with allies to protect our national security and address global challenges to the steel and aluminium industries".
But Canada, Mexico and the European Union have insisted they will not accept quotas to gain permanent exemptions from the US tariffs.
Canadian Prime Minister Justin Trudeau said on Monday that any move by the United States to impose tariffs on Canadian steel and aluminum would be a "very bad idea" guaranteed to disrupt trade between the two countries.
If the EU is subject to tariffs on the 6.4 billion euros ($A10.3 billion) of the metals it exports annually to the US, it has said it will set its own duties on 2.8 billion euros of US exports of products ranging from makeup to motorcycles.