The Prime Minister of the United Kingdom Boris Johnson and the President of the European Commission Ursula von der Leyen spoke to each other by telephone on Saturday.
The aim was to find a common way forward in the negotiations on a trade and cooperation agreement following the UK's withdrawal from the EU earlier this year.
The conversation resulted in a joint statement on Saturday night.
There, Johnson and von der Leyen state that Brexit negotiations will resume on Sunday and that they welcome the progress made in several areas.
"But there are still significant differences in three critical issues: trade conditions, governance and fisheries," the leaders wrote in the statement.
New calls tomorrow
Both parties emphasize that it is not possible to reach an agreement if it is not possible to reach a consensus on the crucial contentious issues.
EU chief negotiator Michel Barnier and Britain's counterpart David Frost will now return to the negotiating table in Brussels on Sunday, Johnson and von der Leyen say.
At the same time, the Prime Minister and the President of the European Commission will follow up Saturday's talks on Monday.
Taxes on goods can be introduced
The Brexit negotiations were suspended on Friday after the parties failed to reach a solution on which rules will apply to fishing, trade and other cooperation between the parties from 1 January 2021.
Britain formally left the EU in an orderly fashion on 31 January this year.
Since then, the parties have tried to agree on a trade and cooperation agreement ahead of Britain's withdrawal from the EU's internal market and customs union last December.
If an agreement is not in place before 1 January, border controls and taxes will be imposed on goods transported between the parties.
Earlier on Saturday, The Guardian reported, citing government sources, that the probability of the parties reaching an agreement is now no greater than 50 percent.