Russian police spokeswoman Irina Volk says Tajikistan's Interior Ministry will send its top expert in battling organised crime to help investigate the incident.
As many as three people were killed and two dozen others were injured in a massive free-for-all brawl between rival ethnic groups at a cemetery in southwest Moscow.
About 200 people, some armed with guns and other weapons, took part in the clashes at the vast Khovanskoye cemetery on Saturday.
More than 90 people, mostly ethnic Chechens, Dagestanis, Uzbeks and Tajiks, were detained after riot police intervened.
A Reuters report says witnesses saw a young man's body lying on the pavement near an overturned car as a forensic expert bent over it. About 10 mainly young men lay handcuffed on the ground while police armed with Kalashnikov rifles looked on.
Pictures posted on social media showed young men wielding iron rods, spade shafts and baseball bats as they rushed into the fighting.
A cemetery official, quoted by Russian RIA news agency, said people from Russia's North Caucasus regions of Chechnya and Dagestan attacked migrants from ex-Soviet Uzbekistan and Tajikistan working there, attempting to take over their jobs.
With Russia's economy battered by Western sanctions and low prices for its oil exports, migrants struggle to find work and ethnic criminal groups add to social tensions.
Tajikistan's Interior Ministry will send to Moscow its top expert in battling organised crime in the former Soviet Union to help investigate the incident, Russian news agencies quoted Russian police spokeswoman Irina Volk as saying.