The decisions came just hours before temporary exemptions from the tariffs on these countries were set to expire on Tuesday.
In a statement, the White House said the details of the deals with Brazil, Argentina and Australia would be finalized shortly, and it did not disclose terms.
The White House added: “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 transshipment, and protect the national security. There would be no further extensions beyond June 1 to stave off tariffs.
On 23 March Trump imposed a 25 percent tariff on steel imports and a 10 percent tariff on aluminum, but granted temporary exemptions to Canada, Mexico, Brazil, the EU, Australia and Argentina.
The U.S. president has invoked a 1962 trade law to erect protections for U.S. steel and aluminum producers on national security grounds, amid a worldwide glut of both metals that is largely blamed on excess production in China.
The tariffs, which have increased frictions with U.S. trading partners worldwide and have prompted several challenges before the World Trade Organization, are aimed at allowing the two U.S. metals industries to increase their capacity utilization rates above 80 percent for the first time in years.