British Prime Minister Theresa May warned the sovereignty of Gibraltar will not be up for negotiation in the Brexit talks as she met European Council president Donald Tusk for the first time since triggering Article 50.
Following the meeting, European Union sources said both sides had recognised the need to "lower tensions" on contentious issues like the future of the Rock.
However, Downing Street said Mrs May had made clear there could be no change to its status without the consent of its people.
The talks came after Mr Tusk suggested last week that Spain - which also claims sovereignty of Gibraltar - could veto its inclusion in any trade deal between Britain and the remaining EU member states.
The move caused fury in Gibraltar - which accused the EU of "bullying" – while a former Conservative Party leader even suggested Mrs May could go to war to defend the Rock.
While few expect it to come to an armed conflict, there is concern among some MPs the EU intends to use the issue as leverage in the Brexit talks.
In a statement following the meeting, a Downing Street spokesman said Mrs May had been clear she was determined to achieve the "best possible deal" for Gibraltar as well as the UK.
"The PM also made clear that on the subject of Gibraltar, the UK's position had not changed: the UK would seek the best possible deal for Gibraltar as the UK exits the EU and there would be no negotiation on the sovereignty of Gibraltar without the consent of its people," the spokesman said.
EU sources said it had been a "good and friendly" meeting, with the talks running on for almost two hours.
"They agreed to stay in regular contact throughout the Brexit process to keep a constructive approach and seek to lower tensions that may arise, also when talks on some issues like Gibraltar inevitably will become difficult," one source said.
The Downing Street statement also said Mrs May reiterated her desire to secure a "deep and special partnership" with the remaining 27 member states, welcoming the European Council's "constructive approach" to the negotiations.
"Both leaders agreed that the tone of discussions had been positive on both sides and agreed that they would seek to remain in close touch as the negotiations progressed," a spokesman said.
