Members of the Visegrad group, or V4, from Hungary, Poland, Slovakia and Czech Republic said they would veto agreements if its citizens working and living in Britain were not treated fairly.
"V4 countries will be uncompromising. Unless we feel a guarantee that these people (living and working in Britain) are equal, we will veto any agreement between the EU and Britain. I think Britain knows this is an issue for us where there's no room for compromise," said Slovak Prime Minister Robert Fico.
The leaders met over the weekend and touched on the matter of Brexit briefly, according to Reuters.
Britain is edging closer to triggering Article 50, the formal start of official negotiations for leaving Europe. Over the weekend the president of the European council, Donald Tusk, said Article 50 would be triggered by Prime Minister Theresa May in early 2017, as soon as January or February, following a meeting between EU leaders about Brexit, but not including Britain.
Downing Street has sought to debunk Tusk's comments, however, claiming it was his own "interpretation" of conversations.