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.
Tension spreading
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.