First funerals of some of the blasts victims took place on Wednesday
Chechen rebel leader Doku Umarov has said his group was behind Monday's double suicide bombings on the Moscow Metro, which left 39 people dead.
In a video message posted on a Chechen rebel website, he said he had personally ordered the attacks.
He said they were carried out to avenge the killings of "poor Chechens" by Russian security forces in February and warned Russia to prepare for more.
The message came as Russia buried the first victims of Monday's attacks.
Russian investigators have said they believe two female suicide bombers were linked to militants in the North Caucasus.
Prime Minister Vladimir Putin has called on the security forces to "scrape from the sewers" those responsible.
In a separate development, at least 12 people, including a top local police official, were killed by two suicide bombings in Russia's North Caucasus republic of Dagestan.
A car bomb was detonated at about 0830 (0430 GMT) outside the offices of the local interior ministry and the FSB security agency in the town of Kizlyar.
Another bomber then blew himself up 20 minutes later as a crowd gathered.
So far no-one has claimed responsibility for the Dagestan blasts.
It was not possible to confirm independently that the man in the video - posted on a rebel website - was Doku Umarov.
He said the Moscow attacks were an act of revenge for the killings of poor Chechen and Ingush civilians by the Russian security forces near the town of Arshty on 11 February.
He said the civilians were "massacred by Russian occupiers" as they were gathering wild garlic to feed their families.
The rebel, who styles himself as the Emir of the Caucasus Emirate, said attacks on Russian soil would continue.
"The war will come to your street... and you will feel it on your own skins," he warned Russian citizens in the video, which he said was recorded on Monday - just hours after the Metro attacks.
Earlier on Wednesday, Doku Umarov's spokesman had told Reuters that his militant group "did not carry out the attack in Moscow, and we don't know who did it".