A group of Central European EU members known as the Visegrad Four is ready to veto any Brexit deal that would limit people's right to work in the UK, Slovakian PM Robert Fico says.
In an interview with the Reuters news agency, Mr Fico said Hungary, Poland, the Czech Republic and Slovakia would be uncompromising in negotiations.
His comments come a day after the EU's first major meeting without the UK.
Brexit, though not formally discussed, overshadowed the Bratislava summit.
At an end of the summit on Friday, Mr Fico said that he and other Central European leaders whose citizens make up much of the EU migrant population in Britain would not let those people become "second class citizens".
But in the interview with Reuters news agency on Saturday, he went further.
"V4 [Visegrad group] countries will be uncompromising," he said. "Unless we feel a guarantee that these people are equal, we will veto any agreement between the EU and Britain."
However, a Slovak foreign ministry source told the BBC Mr Fico had been referring only to those EU citizens living in the UK at the time of the referendum.
The Czech ambassador to the UK, Libor Secka, pointed out this was not an "official statement" of the Visegrad countries' common position on their approach to Brexit negotiations.
He said that while he respected Mr Fico's opinion, it was for Poland - which holds the Visegrad presidency - to speak on behalf of the group.
"We are not going to provide a running commentary on these negotiations," said a British government spokesman when contacted by the BBC. "That approach won't help us get the best deal for Britain."
All the EU leaders have insisted there will be no formal Brexit talks until Britain triggers the two-year divorce process and says what it wants.
European Council President Donald Tusk, said the British Prime Minister Theresa May had recently told him that might be in January or February 2017.
The Bratislava summit was intended as a discussion about the best way forward, following Britain's vote to leave the bloc.
In particular, leaders tried to find common ground on the best way to deal with the numbers of migrants coming into Europe, and how to deal with the after effects of several years of economic crisis.
The Visegrad group has consistently opposed EU efforts to introduce mandatory quotas for migrants.
But in the interview, Mr Fico said the EU had shifted from a debate over mandatory quotas to a new principle of "flexible solidarity" over the migrant crisis.
He said he did not get everything he wanted, but he was happy that a debate had begun on flexible solidarity, allowing countries to offer what they can to tackle the migrant crisis.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.