Russia in past years has seen a series of terror attacks on buses, trains and airplanes, some carried out by suicide bombers.
Twin bombings on the Moscow subway in March 2010 by female suicide bombers killed 40 people and wounded more than 120. In January 2011, a male suicide bomber struck Moscow's Domodedovo Airport, killing 37 people and injuring more than 180.
Umarov, who had claimed responsibility for the 2010 and 2011 bombings, ordered a halt to attacks on civilian targets during the mass street protests against Putin in the winter of 2011-12. He reversed that order in July, urging his men to "do their utmost to derail" the Sochi Olympics, which he described as "satanic dances on the bones of our ancestors."
The International Olympics Committee expressed its condolences over Sunday's bombing in Volgograd, but said it was confident of Russia's ability to protect the Games.
Russian Olympic Committee chief Alexander Zhukov said Monday there was no need to take any extra steps to secure Sochi in the wake of the Volgograd bombings, as "everything necessary already has been done."
Russian authorities have introduced some of the most extensive identity checks and sweeping security measures ever seen at an international sports event.
Anyone wanting to attend the games that open on Feb. 7 will have to buy a ticket online from the organizers and obtain a "spectator pass" for access. Doing so will require providing passport details and contacts that will allow the authorities to screen all visitors and check their identities upon arrival.
The security zone created around Sochi stretches approximately 100 kilometers (60 miles) along the Black Sea coast and up to 40 kilometers (25 miles) inland. Russian forces include special troops to patrol the forested mountains flanking the resort, drones to keep constant watch over Olympic facilities and speed boats to patrol the coast.
The security plan includes a ban on cars from outside the zone from a month before the games begin until a month after they end.
Associated Press writer Jim Heintz contributed to this report.
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