By Laurence Norman in Brussels and Max Colchester in London

U.K. Prime Minister Boris Johnson is set to hold talks with top Brussels officials later this month in a bid to break an impasse in negotiations on a post-Brexit trade deal, after the latest round ended Friday with no major breakthrough.

The European Union's chief negotiator, Michel Barnier, said the negotiations needed some "extra political momentum" if the gaps between the two sides on key issues are to narrow.

"This week there has been no significant areas of progress," Mr. Barnier said. David Frost, the British chief negotiator, said, "Progress remains limited."

After the U.K. left the bloc at the end of January, the two sides entered a transition period lasting until end of the year, during which their commercial relations remained unchanged. That period can be extended for up to two years, but only if both sides agree to do so by the end of this month.

Mr. Johnson has said his government won't ask for an extension, but the negotiations have been hampered by the coronavirus pandemic, during which the two sides have negotiated remotely.

British officials said they would continue to talk through the summer, backing away from an earlier claim that they would shelve the discussions if progress wasn't made by the end of this month.

Without an extension, the two sides have until the end of the year to agree on a new set of rules governing Britain's access to the EU's single market and cooperation on law enforcement, criminal justice, energy and fisheries, among other things.

Failure to reach an accord would mean quotas and tariffs being imposed on trade between Britain and the bloc. Investors are beginning to worry about supply-chain disruption at end of the year, compounding the hit to the economy caused by the pandemic and hurting Britain more than its neighbors.

EU and British officials have said they are expecting talks between Mr. Johnson, European Commission President Ursula von der Leyen and other top officials in coming weeks, although no date has yet been set. The top negotiators could also meet for face-to-face talks in coming weeks.

Mr. Johnson, who himself was hospitalized with Covid-19, hasn't yet weighed into the negotiations.

The two sides remain divided on a series of issues. The U.K. rejects an EU demand that it commit to specific labor, environmental, state-aid and other standards as part of an agreement, and is calling for an overhaul of fisheries rules to give greater rights to British fleets. Britain insists it won't accept the jurisdiction of the European Court of Justice as part of the deal.

The EU insists it wants one agreement with one oversight body, while Britain wants a series of deals governing different areas of cooperation.

Mr. Frost said the negotiations were reaching the limits of what could be achieved remotely, and that work should be intensified and accelerated.

Nonetheless, there were hints of compromise that could prove important. Mr. Barnier signaled the EU might scale back its demand that U.K. state-aid rules continue to mirror European ones. He has also suggested a willingness to compromise over the U.K.'s fisheries demands, though that is facing some resistance from the bloc's member states, diplomats have said.

A senior U.K. official said the focus was on wrapping up talks by the fall. British officials hope that the EU will agree to loosen level-playing-field rules in return for tariffs on a small number of goods. So far, this hasn't gained traction with EU negotiators.

Mr. Barnier said he expects that, if an agreement is reached, the two sides will still be in intensive discussions as late as October.

Write to Laurence Norman at laurence.norman@wsj.com and Max Colchester at max.colchester@wsj.com