Following a two-hour meeting at Downing Street, EU sources said both leaders accepted the need to tone down the rhetoric following the posturing over the future of the Rock.
However, Downing Street later said the Prime Minister had made clear to Mr Tusk that there could be no change to the status of the British enclave without the consent of its people.
In a draft set of guidelines for upcoming Brexit talks, Mr Tusk last week suggested that Spain could be given a veto over how any future trade deal between the UK and the EU would apply to Gibraltar.
It sparked fury on the Rock, where the Chief Minister accused the EU of “bullying” and behaving like a “cuckolded husband”. Former Conservative Party leader Lord Howard even suggested Mrs May could go to war, forcing Downing Street to deny it would send a naval taskforce to defend the territory.
In a statement, a No 10 spokesman said the Prime Minister 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. “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 was quoted as saying.
Number 10 added that “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.”