The EU has expressed concern after Bosnian Serbs decided to suspend co-operation with the country's central police force and courts.
The decision could "jeopardize the functioning of the judiciary and law enforcement in BiH [Bosnia-Herzegovina]", the EU warned.
The Bosnian Serb move follows raids by officers investigating war crimes.
Most Bosnian Serbs live in one of two entities set up by the Dayton agreement that ended the 1992-1995 Bosnian war.
Tensions have been rising for several months after lawmakers in the Bosnian Serb Republic, or Republika Srpska, voted to hold a referendum on the authority of Bosnia's national court in their entity.
Bosnian Serb President Milorad Dodik, who proposed the referendum, said the country's prosecutors had been more lenient towards "the few Bosniaks" charged with war crimes compared with Serbs.
On Thursday Bosnian Serb Interior Minister Dragan Lukac decried raids by state investigators looking for Bosnian Serb suspects in the town of Novi Grad as "inappropriate and provocative".
Supporting the move to suspend law-enforcement co-operation, Mr Dodik said the operation constituted an attack "that could even have provoked armed conflict".
But in a statement, the EU called on authorities in Bosnia-Herzegovina to "maintain mutual co-operation and dialogue".
It underlined "the need to respect the rule of law throughout the whole territory of the country".
Bosnia became an independent state after the war, but half its population - around two million people - had been displaced, and its infrastructure and economy was left in tatters.
Its political set-up is complicated, with the two regions having their own governments, parliament, police and other bodies - linked to a central Bosnian government and rotating presidency.
The country has been encouraged to seek membership of the European Union to strengthen its stability, but it has been unable to escape high levels of corruption, unemployment and political divisions that have put off foreign investors.