May told Chief Minister of Gibraltar Fabian Picardo that "we will never enter into arrangements under which the people of Gibraltar would pass under the sovereignty of another state against their freely and democratically expressed wishes."
The European Union has said that Spain would have to agree to extend any trade deal between the bloc and Britain to also cover the 6.7-square-kilometre (2.6-square-mile) British overseas territory on the southern tip of Spain.
This means that Madrid could potentially block Gibraltar's access to any trade deal, and politicians in "the Rock" fear that Madrid will use the veto to seek sovereignty over the peninsula.
May told Picardo that she would never "enter into a process of sovereignty negotiations with which Gibraltar is not content," according to a readout of the phone call released by her Downing Street office.
"The UK remains steadfastly committed to our support for Gibraltar, its people and its economy," it added.
British foreign minister Boris Johnson earlier Sunday stressed that the territory "will not be bargained away".
"Gibraltar is not for sale. Gibraltar cannot be traded. Gibraltar will not be bargained away," Johnson wrote in the Sunday Telegraph.
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