The governor of the northern Russian region of Karelia - scene of recent ethnic violence - has blamed migrants for most of the unrest.
Sergei Katanandov said the behaviour of some young people from the Caucasus was inexcusable, and they would have to lower their profile or leave.
Riots erupted after two Russians were killed last week in a cafe fight with Chechens in the town of Kondopoga.
Chechen leaders have blamed the police for failing to contain the unrest.
A Chechen delegation has arrived in Karelia on a fact-finding mission.
"We will certainly visit Kondopoga to meet and speak to the local population," Idris Usmanov, deputy speaker of the Chechen assembly told Itar-Tass news agency.
"The events similar to those in Kondopoga should never happen again in any Russian region," he said.
In an interview with the Isvestia newspaper, Karelia's governor also criticised local police and prosecutors for allowing the cafe brawl to snowball out of control.
But he put the blame mostly on the migrants from the Caucasus.
"Some of these people will probably have to change their place of residence. These young people will either have to behave quietly and keep their heads down or leave," Mr Katanandov said.
The authorities and human rights groups have warned that the racial violence in Karelia could spread, the BBC's James Rodgers reports from Moscow.
On Tuesday night, supporters of far-right movements held a rally in the regional capital of Petrozavodsk, about 100km (60 miles) from Kondopoga.
White supremacist groups in Russia have openly encouraged attacks on non-Slavs in recent years.
There have been countless beatings, and several deaths - but the numbers involved in the latest unrest appear unprecedented.