BRUSSELS—The European Union wants to expand its dialogue with Russia on key foreign policy issues, the first significant sign of a thaw in relations and a move that reflects growing concerns in Brussels about U.S. foreign policy.

EU foreign policy chief Federica Mogherini said she discussed the issue with her Russian counterpart, Sergei Lavrov,  on Monday in Moscow, the first formal bilateral visit to Russia by a top EU official since the Ukrainian crisis erupted in early 2014.

The EU has for some time been exploring a reopening of formal channels of communication that were cut after Moscow’s annexation of Crimea and its intervention in eastern Ukraine. Before that, the EU and Russia held regular summits that dealt with issues from energy and foreign policy to economic cooperation and trade.

Ms. Mogherini worked closely with Mr. Lavrov during the Iranian nuclear talks and they have met and spoken frequently on such issues as the Syrian civil war and the Libyan conflict. However, with the EU imposing economic sanctions on Russia in 2014 over its actions in Ukraine and with Moscow firing back with its own ban on European agricultural imports, those conversations have remained ad hoc.

A number of European capitals have called for greater political engagement, including some that firmly support the bloc’s economic sanctions.

Ms. Mogherini said now is the time to move ahead.

“We discussed the possibility to intensify, to have more regular exchanges on foreign policy issues, which is exactly in our interests,” Ms. Mogherini said, specifically mentioning Syria, the Middle East, Iran, Libya, Afghanistan and North Korea.

No detailed plans have yet been elaborated, officials said. Mr. Lavrov said Monday his government has always favored retaining the full range of dialogue with the EU.

The North Atlantic Treaty Organization last year resumed meetings with Russian officials through the NATO-Russia Council, and the two sides have begun more regular meetings.

When they restarted, the council was a forum for each side to lecture the other on Ukraine, Afghanistan and other contentious issues. The meetings have since become more regular and emerged as a forum for each side to discuss its military buildup and exercises, in an effort to increase transparency.

For Brussels, stepped-up discussions with Russia would broaden the bloc’s options at a time when the Trump administration has sent mixed signals about its desire to work with the EU.

On a number of issues, including support for the Iranian nuclear deal and backing for a two-state solution in the Middle East, the EU’s foreign policy positions are closer to Moscow’s than to Washington’s. Ms. Mogherini reiterated Tuesday that the EU fully supported the nuclear deal.

President Donald Trump said last week it was possible the U.S. could withdraw from the nuclear deal, which he has described as a terrible agreement.

Ms. Mogherini said in a December interview that the EU was ready for a more “transactional way of working” with Washington under Mr. Trump and that, where necessary, it would cooperate with Moscow to defend the EU’s views and interests.

Still, the prospect of genuinely closer ties with Moscow looks distant for now. In addition to continued EU sanctions on Russia, Brussels is backing a transition away from the Assad regime in Syria while Russia is heavily involved militarily in shoring up the Syrian government.

The EU still has major trade disputes with Russia, and European leaders from Berlin to Stockholm have raised alarms about alleged Russian cyberattacks, political interference and military threats.