Theresa May has said she "wants and expects" to be able to protect the rights of Polish citizens in the UK, if British expats' rights are protected.
In Poland on the latest visit of her post-referendum tour of EU leaders, the UK prime minister said she valued Poles' contribution to the UK.
There are more than 850,000 Poles in the UK, official figures say - the largest group of EU nationals by far.
Mrs May met PM Beata Szydlo in Warsaw after meeting Slovakian PM Robert Fico.
She started by paying tribute to Polish pilots who fought alongside the British in World War Two and said the partnership between the two countries would "endure long after the United Kingdom has left the European Union".
Of the hundreds of thousands of Polish citizens living and working in the UK, she said: "I want and expect to be able to guarantee their rights in the UK.
"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."
The UK PM said she wanted to "make a success of Brexit" and would "seek to address the concerns of the British people about free movement" while working for a "close economic relationship with the EU".
"Of course there will be different interests and complex issues to resolve but I firmly believe that if we approach this in a constructive and positive spirit then we can pave the way for a calm and orderly departure,
"And in that context 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. We condemned the shameful and despicable attacks against Polish communities and others in the wake of the referendum result.
"Hate crime of any kind directed against any community, race or religion has absolutely no place in British society."
Earlier, following talks with Slovakian PM Robert Fico in Bratislava, she stressed that British voters had sent a "very clear message" about wanting more control over EU migration into the UK.
"We will be looking to deliver that as part of our negotiations as well as looking for the best possible deal on trade in goods and services".
The UK prime minister stressed, at a press conference with Mr Fico, that the UK was "not leaving Europe or withdrawing from the world".
"Once we have left the EU we will continue to work with our partners across Europe, indeed Brexit is an opportunity to intensify those relationships."
The economic relationship between the UK and Slovakia was "flourishing", she said, with a 37% rise in UK exports to the country last year and investment by British firms such as Tesco and Jaguar Land Rover.
"So it matters to both of us that we maintain the closest possible economic relationship once the UK has left the EU."
She also reiterated that she wanted to protect the rights of EU citizens in the UK, providing the rights of UK citizens in EU countries are also protected. She said she had discussed the matter with Mr Fico and "that concept of reciprocity is recognised."
The Slovakian PM said he had asked Mrs May "to dedicate a special level of attention to Slovak nationals and citizens who work currently in the UK" and said he hoped the UK would "redefine" and formulate "a vision of its relations with the EU" before triggering Article 50 - the formal process of leaving the EU.