UPDATE 1-Top U.S., EU officials fix meeting next week on tariffs - EU source

(Adds more on meeting, background on dispute)

BRUSSELS, March 15 (Reuters) - U.S. Commerce Secretary Wilbur Ross and European Trade Commissioner Cecilia Malmstrom have agreed to meet next week in an attempt to resolve a deepening dispute over trade tariffs, a European Commission source said on Thursday.

Ross and Malmstrom spoke on the telephone on Thursday and discussed U.S. plans to impose import duties of 25 percent on steel and 10 percent on aluminium, the source said.

Malmstrom repeated the European Union's hope that it would be exempted, given that the bloc is a close security ally of the United States, and said the two should work together on the issue of global overcapacity, which was harming both economies.

President Donald Trump, who has cited national security for imposing the tariffs, has already offered exemptions to Canada and Mexico.

Ross and Malmstrom agreed to meet next week although details of the talks remain to be set, the Commission source said.

Malmstrom met U.S. Trade Representative Robert Lighthizer in Brussels on Saturday, but emerged from that meeting saying it was not clear how the EU could seek exemptions.

Trump tweeted on Monday that Ross would lead Washington's efforts to persuade the EU to remove tariffs and barriers that he has described as "horrific" and unfair to U.S. farmers and manufacturers.

He has also threatened to set import levies on EU cars.

The EU disputes Trump's line on tariffs and his emphasis on cars, for which the U.S. tariff, at 2.5 percent, is lower than the EU's 10 percent. For other products, U.S. tariffs are higher, such as trucks at 25 percent compared with an EU rate that can be as low as 10.

The Commission has said that, if the United States applied tariffs to EU steel and aluminium, then it would launch a legal challenge at the World Trade Organization and consider its own tariffs or quotas to prevent those metals flooding into Europe.

It has also drawn up a list of U.S. products worth 2.8 billion euros ($3.45 billion) on which it could impose 25 percent import duties. ($1 = 0.8112 euros) (Reporting by Philip Blenkinsop; editing by Foo Yun Chee and David Stamp)