Prime Minister Boris Johnson European Commission president Ursula von der Leyen spoke via video conference on Saturday as negotiations reach a critical point with less than two weeks remaining before the agreed mid-October deadline.
The joint statement revealed gaps still remain "notably but not only" in the areas of fisheries, the level playing field, and governance.
The final scheduled round of talks between Brussels and the UK concluded this week, but both sides plan to continue talking until the EU leaders' summit on 15 October - just 12 days away.
The two leaders have tasked chief negotiators, Britain’s Lord Frost and the EU’s Michel Barnier, with intensifying the talks after acknowledging that “significant gaps remained” between the UK and Brussels.
Ms von der Leyen, after speaking with Mr Johnson, tweeted to say it had been a "good phone call.
She added: "While progress had been made, significant gaps remain. We agreed that it's important to find an agreement as strong basis for a strategic relationship."
A Downing Street spokesman said: “They agreed on the importance of finding an agreement, if at all possible, as a strong basis for a strategic EU-UK relationship in future.
“They endorsed the assessment of both chief negotiators that progress had been made in recent weeks but that significant gaps remained, notably but not only in the areas of fisheries, the level playing field, and governance.
“They instructed their chief negotiators to work intensively in order to try to bridge those gaps.
“They agreed to speak on a regular basis on this issue.”
Political Correspondent Daniel Hewitt explains the latest Brexit developments:
In a statement issued after his meeting with EU chief negotiator Michel Barnier on Friday, Lord Frost said that while the “outlines” of an agreement were “visible”, there were still “familiar differences” to be overcome.
Lord Frost added that there had been “some limited progress” on state aid while the gap over fisheries was “unfortunately very large” and may prove “impossible to bridge”.
“I am concerned that there is very little time now to resolve these issues ahead of the European Council on October 15,” he said.
Irish Taoiseach Micheal Martin, who briefed other EU leaders with Mrs von der Leyen on the state of the negotiations, said it was “highly unlikely” there would be an agreement by October Council meeting, although there would need to be significant progress in the coming weeks.