Doku Umarov, a Chechen separatist leader, claimed in a video posted on Wednesday on www.kavkazcenter.com, an unofficial separatist website, that he had ordered the Moscow attacks in revenge for Russia's policies in the mainly Muslim North Caucasus.
'Scraped from sewers'
The North Caucasus has been the site of two wars in Chechnya and hundreds of violent attacks since the 1991 collapse of the Soviet Union.
Violence has spread from Chechnya to the neighbouring regions of Dagestan and Ingushetia.
Vladimir Putin, Russia's prime minister, tightened his power in 1999 by launching his country's attempt to crush Chechen separatism.
Earlier this week he said the culprits behind the metro bombings in Moscow must be scraped "from the bottom of the sewers".
Rights groups say Russia's violent policies in the North Caucasus have failed to deal with the root causes of the Muslim uprising.
Local leaders and residents say it is fuelled by poverty, clan rivalries, rampant corruption, Islamism and heavy-handed tactics by law-enforcement agencies.
In November, Medvedev warned that escalating strife in the region was Russia's most serious domestic political problem and has spoken about the need to fight poverty and corruption.
Alexander Khloponin, the president's newly appointed envoy to the region, said stability would be elusive until officials earned the support of local residents.
"We will never cope with this task if we do not have the full support of our residents," Khloponin said.
On Thursday, another explosion in Dagestan killed two suspected Chechen fighters and wounded a third.
Police said the men may have been transporting a makeshift bomb.