Charles Michel, President of the European Council, and Ursula von der Leyen, President of the European Commission, addressed the 27 member leaders on Friday. The EU face a deadline at the end of the year when the Brexit transition period will be over.
So far, the UK Government have told the EU they do not want an extension to the transition period.
However, Brexit deal talks between the two sides have yet to be successful.
Ms von der Leyen told the news conference: “We jointly stressed our willingness to undertake all possible efforts to come to an agreement.
“For this we have to bridge wide divergences, which remain to be solved.”
Mr Michel reiterated this message by saying that the EU trade bloc wanted a new deal with Britain, “but not at all costs”.
He said: “We need to intensify the negotiation.”
Mr Michel also noted that the UK Prime Minister Boris Johnson had refused to ask for extra time for the talks.
The EU is seeking close ties for the future relationship to cover climate, fishing, transport and security.
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In the Brexit transition period Britain remains in the single market and customs union.
By the end of the year, when the transition period is over, EU rules will no longer directly apply in Great Britain.
New goods trade rules will be introduced gradually.
This week, UK and EU leaders said that new momentum is needed in Brexit negotiations.
After virtually meeting Ms von der Leyen at the start of the week, Mr Johnson said there was a very good chance of achieving a trade deal by December.
Ms von der Leyen also said both sides had agreed to deliver the best deal for citizens.
In a joint statement following Monday’s virtual meeting, the UK and EU said they “welcome the constructive discussions on the future relationship that has taken place”.
The statement continued: “The parties agreed nevertheless that new momentum was required.”
Both sides have agreed to intensify negotiations in July.
The UK Government said the negotiations will involve formal talk rounds and smaller group meetings in London and Brussels depending on coronavirus guidelines.