At a meeting in Downing Street, the Prime Minister insisted there could be no change to the status of the Rock without the consent of its people.
Her comments came during a face-to-face meeting in Downing Street to discuss "the way ahead on Brexit".
A No 10 spokesman said: "The PM 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."
It is the first time Mrs May has met Mr Tusk since she wrote him a letter triggering Article 50 on March 29. Mr Tusk sent his own written response to Mrs May two days later.
The meeting has been seen as an important step in getting the two-year Brexit negotiations underway.
A Downing Street spokesperson said: “The PM reiterated the UK’s desire to ensure a deep and special partnership with the European Union following its exit, and noted the constructive approach set out by the Council in its draft guidelines published last week.
“She said the UK looked forward to formally beginning negotiations once the 27 Member States agreed guidelines.
"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.
Meeting PM May to make sure Brexit talks get off to good start. Agreed to stay in regular contact throughout process https://t.co/udh7VEsoHy— Donald Tusk (@eucopresident) April 6, 2017
Number 10 officials said the meeting was "not the beginning of thrashing things out" but would be "a general discussion on the content of the letters".
Mr Tusk has made it clear that while he is seeking a fair settlement, the Brexit talks could become confrontational at times.
He has indicated that talks on a trade deal could begin this autumn, but only if "sufficient progress" has been achieved in negotiations on the arrangements for Britain's withdrawal - widely seen as a reference to agreement on a "divorce bill" of an estimated £50 billion.
Mrs May has said that by Brexit Day in March 2019 she expects the shape of a new UK-EU trade relationship to be clear, but appeared to accept that the formal conclusion of any agreement will have to wait until after withdrawal.
Speaking before the meeting, Mrs May told an audience in Nottingham: "We will be talking about the start of the negotiations and how we are going to be taking those negotiations forward.
"I have obviously sent the letter to invoke Article 50, we have said very clearly we want to maintain a deep and special partnership with the EU and I think that has been reciprocated.
"I'll be talking with President Tusk about how we can ensure, within the timescale we have got, that we can deliver a deal that is going to work for the people of the United Kingdom, but I believe that will also be a deal that will work for the EU as well."