"I want to be clear that Poles living in the UK continue to be welcome and we value the contribution they make to our country," May said on Thursday during a joint press conference with Polish Prime Minister Beata Szydlo
There are some 850,000 Poles living in Britain, according to official figures say. Poles make up by far the largest community of EU nationals and Polish is the second-most spoken language there.
"I fully expect and intend to be able to guarantee the rights of Polish citizens when we leave the EU," May said, but demanded a reciprocal process.
"The only circumstances in which that would not be possible would be if the rights of British citizens living across the EU were not guaranteed," she said.
In the June 23 referendum, about 52 percent of British voters opted to leave the EU, while roughly 48 percent of the people voted to stay in the union.
Those in favor of a British withdrawal from the EU argued that outside the bloc, London would be better positioned to conduct its own trade negotiations, better able to control immigration and free from what they believe to be excessive EU regulations and bureaucracy.
Those in favor of remaining in the bloc argued that leaving it would risk the UK's prosperity, diminish its influence over world affairs, and result in trade barriers between the UK and the EU.
After the Brexit vote, the British pound crashed to its lowest levels in 31 years, dropping below $1.35 for the first time since 1985.