"At the moment, we have 26 injured and three dead," Interfax news agency said, quoting a spokesman for Moscow's health department.
Twenty-three people were hospitalised, four of them with serious injuries, the official said.
An earlier toll by police gave two dead and 10 injured, along with 50 arrests.
Reports said the fight at the Khovanskoye cemetery involved 200 immigrants from former Soviet Central Asia and residents from Russia's volatile North Caucasus.
Footage shown on the TV news channel LifeNews showed dozens of men armed with staves or steel bars in running battles inside the cemetery and at its entrance.