In addition to the dead, the bombings wounded 104 people, according to Russia's Health Ministry. As of late Monday, 58 remained hospitalized, many in grave condition.
Suicide bombings have rocked Russia for years, but the insurgents seeking to create an Islamic state have largely confined their attacks to the North Caucasus region in recent years. The blasts in Volgograd signaled that militants want to show their reach outside their native region.
A city of 1 million northeast of Sochi, Volgograd is a hub with railway lines running in five directions across the country and numerous bus routes connecting it to the volatile Caucasus provinces.
Security checks on buses have remained largely symbolic and easily avoidable, making them the transportation mode of choice for terrorists in the region. Tighter railway security isn't always enough to prevent casualties. In Sunday's attack, a suicide bomber detonated an explosive in front of the train station's metal detectors, killing 17 people, including the attacker.
In October, a suicide bombing on a bus in Volgograd killed six people.
Security at Russia's railway stations and airports has been tightened after a suicide bomber hit Moscow's Domodedovo Airport in January 2011, killing 37 people and injuring more than 180. Two bombings on the Moscow subway in March 2010 by female suicide bombers killed 40 people and wounded more than 120.
Umarov, who had claimed responsibility for the 2010 and 2011 bombings, ordered a halt to attacks on civilian targets during the mass demonstrations 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."
Aware of the threat, the Sochi organizers 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 will have to buy a ticket online from the organizers and obtain a "spectator pass" for access. Doing so will require providing passport details that allow authorities to screen all visitors.
The security zone created around Sochi stretches approximately 60 miles along the Black Sea coast and up to 25 miles inland. Russian forces including special troops will patrol the forested mountains flanking the resort and use drones to keep a constant watch over Olympic facilities. Speedboats will patrol the coast and sophisticated sonar will be used to detect submarines.
Cars from outside the Olympic zone will be banned beginning a month before the Winter Games, and Sochi residents are already facing widespread identity checks.
The White House said the U.S. would welcome "closer cooperation" with Russia on security preparations for the safety of athletes, spectators and other participants at the Olympics following the two attacks.
"The U.S. government has offered our full support to the Russian government in security preparations for the Sochi Olympic Games," White House spokeswoman Caitlin Hayden said.
Some observers have warned that terrorists may simply choose softer targets in the vicinity of Sochi to sow panic.
"Even if they succeed in protecting Sochi, there could be a series of major attacks near Sochi," Anatoly Yermolin, a veteran KGB officer, told Ekho Moskvy radio.
Alexei Filatov, another veteran of the Russian security forces, also predicted that terrorists will try to step up their attacks before the Olympics.
"The terrorist activities will increase as the Sochi Olympics get closer, and they will get increasingly close to the area," Filatov wrote on his blog. "For those who order terror attacks, it serves as an opportunity to deal a blow to Russia on global stage."
Some Russian commentators also have suggested that terrorists could have planted sleeper agents in Sochi long before security was tightened. Others indicated that terror groups could have rigged some Olympic facilities with explosives during construction. Russian officials have denied that could happen, citing stringent security controls at Olympic construction sites.
Russian Olympic Committee chief Alexander Zhukov insisted Monday that there was no need to take any extra steps to secure Sochi in the wake of the Volgograd bombings because "everything necessary already has been done."
International Olympic Committee President Thomas Bach offered his condolences Monday in a letter to Putin and expressed full confidence that Russia would deliver "safe and secure games in Sochi."
Meanwhile, a number of Olympic leaders and federations signaled their confidence in the host country.
"When we come to Sochi, it will be impossible for the terrorists to do anything," Norwegian IOC member Gerhard Heiberg said. "The village will be sealed off from the outside world. Security has been our priority No. 1 ever since Sochi got the games."
U.S. figure skater Ross Miner, who won silver in Vancouver, is well aware of the vulnerability of major sporting events. The theme of the New England native's long program is "Boston Strong," about the city's resilience after the marathon bombings last spring.
Miner recalled the 2011 world championships in Moscow as "by far the most intense security I've ever had at a competition," with skaters going through metal detectors to enter the venue.
At the United Nations, the Security Council condemned the attacks as "heinous and cowardly acts," and Secretary-General Ban Ki-moon spoke to Putin by telephone, offering his condolences and stressing the importance of international cooperation to fight terrorism, according to the U.N. press office.
Russian authorities ordered police to increase security at train stations and other transportation facilities across the country. The heightened security comes as Russians are preparing to celebrate the New Year, the nation's main holiday.
In St. Petersburg, Russia's second-largest city, the local governor canceled a New Year's fireworks show.
Vladimir Markin, the spokesman for Russia's main investigative agency, the Investigative Committee, said Monday's explosion involved a bomb similar to the one used Sunday, indicating that the two attacks were linked.
Markin said a suicide attacker was responsible for Monday's bus explosion that killed at least 14 people. It was not clear if authorities counted the bomber in their death toll.
Associated Press writers Jim Heintz in Moscow and Alexandra Olson at the United Nations contributed to this report.