There will be no negotiation on Gibraltar's sovereignty without the consent of its people, Theresa May has told Donald Tusk.
Draft Brexit negotiating guidelines, sent out on Friday, contained a clause suggesting Spain will be able to veto any future trade deal between the EU and the UK.
Following talks between the Prime Minister and the President of the European Council in Downing Street, a Number 10 spokesperson said that on Gibraltar, Mrs May had made it clear that "the UK's position had not changed".
The spokesperson added that 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".
On Brexit itself, the spokesperson said the Prime Minister had "reiterated" Britain's desire to "ensure a deep and special partnership with the European Union following its exit".
"Both leaders agreed that the tone of discussions had been positive on both sides," they added.
An EU source said the meeting had been "good and friendly", and that both sides had seen the need to "lower tensions" over sensitive subjects like Gibraltar.
"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," the source said.
Mr Tusk tweeted: "Meeting PM May to make sure Brexit talks get off to good start. Agreed to stay in regular contact throughout process."
Spain has a long-standing territorial claim on Gibraltar, which has been held by the UK since 1713 and has the status of a British Overseas Territory.
The former Conservative leader, Lord Howard, has suggested Theresa May would show the same resolve to defend Gibraltar as Margaret Thatcher did over the Falklands.
He told Sky News' Sophy Ridge on Sunday show: "I think there's no question whatever that our Government will stand by Gibraltar.
"Thirty-five-years-ago this week, another woman prime minister sent a task force half way across the world to defend the freedom of another small group of British people against another Spanish-speaking country.
"I'm absolutely certain that our current Prime Minister will show the same resolve in standing by the people of Gibraltar."