But Treasury Secretary Steven Mnuchin said Monday that Trump had not made a decision on the exemptions despite the looming deadline.
Ross also said last week that nations have been asked to accept import quotas in return for tariff-free access of the metals into the U.S. But that suggestion puts the European Union in the hard position of either succumbing to U.S. demands that could breach trade rules or face punitive tariffs.
The confrontation stems from the president's decision in March to slap tariffs of 25 percent on imported steel and 10 percent on imported aluminum.
"We're going to have very frank discussions", Mnuchin in an interview broadcast Monday on Fox Business.
Trump has invoked a 1962 trade law to erect protections for USA steel and aluminum producers on national security grounds, amid a worldwide glut of both metals that is largely blamed on excess production in China.
A Downing Street spokesman said the leaders had spoken of "the vital importance of our steel and aluminium industries and their concern about the impact of United States tariffs" and "pledged to continue to work closely with the rest of the European Union and the U.S. administration with the aim of a permanent exemption from USA tariffs".
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Mr Trump responded by calling for further United States tariffs against China, escalating trade tensions between the two giants. The quota deal came as part of a broader renegotiation on the US and South Korea's bilateral trade deal, KORUS.
The EU on April 16 submitted a request to the World Trade Organization for consultations with Washington to determine whether and how the US can compensate the bloc if trade flows into the EU are affected by the new tariffs. He also granted a permanent exemption to South Korea.
Most administration officials are pushing for Trump to at least extend the exemptions to continue talks on trade remedies, Jonathan Swan of the news website Axios reported.
Steel industry officials said it was possible that some countries could receive longer exemptions, particularly Canada and Mexico, given that the tariff negotiations had become intertwined with talks about updating the North American Free Trade Agreement. The U.S. refused to offer the European Union compensation and said the request for consultations had no basis under WTO rules. The US imposed the tariffs after concluding foreign shipments imperil its security.
The uncertainty over steel tariffs isn't just causing unease among allies.
The Commerce Department says it's already boosted staff, and wants approval from Congress to use more of its budgeted funds to help solve the problem. No decision on a request can be made until it's been reviewed and posted online for 30 days for any objections.