U.S. Secretary of State Rex Tillerson met Thursday with the European Union's chief diplomat, Federica Mogherini, as the two governments struggle to find solid footing despite the U.S. president's support of Britain's decision to leave the EU.

Mogherini's task Thursday was to test the waters for Europe's relationship with the new Donald Trump administration, beginning with Tillerson, the top U.S. diplomat.

EU Top Diplomat Has 'Fruitful' Meeting With US Secretary of State

Afterward, Mogherini pronounced the meeting in Washington, D.C., "fruitful" and said the United States and European Union have many issues on which they would like to cooperate closely.

EU Top Diplomat Has 'Fruitful' Meeting With US Secretary of State

Trump has praised Britain for its Brexit plans and has repeatedly criticized NATO and other European institutions. Trump has also praised Russian President Vladimir Putin, who maintains a tenuous relationship with his European neighbors.

EU Top Diplomat Has 'Fruitful' Meeting With US Secretary of State

While in Washington, D.C., on Thursday, Mogherini also met with members of Congress and was slated to meet with security officials at the White House.