Theresa May told Donald Tusk that there would be no negotiation on Gibraltar's sovereignty without the consent of its people, Downing Street said on Thursday (6 March).
A Number 10 spokesperson also said the UK prime minister stressed to the EU Council president that Britain's position had not change during their summit in London.
"She said the UK looked forward to formally beginning negotiations once the 27 Member States agreed guidelines," the spokesperson said.
"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.
"The prime minister 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 talks between May and Tusk come just a week after the prime minister invoked Article 50 of the Lisbon Treaty and triggered the two-year-long divorce talks with the EU.
The prime minister's Article 50 letter failed to mention Gibraltar, but draft EU Council negotiation guidelines proposed giving Spain a say in The Rock's future relationship with the EU.
An EU source told the Press Association that May and Tusk had decided to "lower tensions" over the issue. Gibraltar, which shares a border with Spain, has been a British overseas territory since the 18th century.
The meeting between May and Tusk comes weeks before the 29 April summit of the 27 other leaders. The top politicians will thrash out negotiating guidelines for the EU Commission, the executive arm of the economic and political bloc.
EU Commission chief Jean Claude Juncker has appointed France's Michel Barnier to lead the talks.
A Downing Street spokesperson added: "The prime minister reiterated the UK's desire to ensure a deep and special partnership with the EU following its exit, and noted the constructive approach set out by the Council in its draft guidelines published last week."
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