The blast tore through a trolleybus near a busy market in the Dzerzhinsky district during the morning rush hour and, in addition to those killed, at least 20 others were injured.
Health Minister Veronika Skvortsova said the patients were in “a bad condition with burns, with multiple injuries typical of blast-induced wounds”.
The attack in Volgograd – which is one of the venues for the 2018 FIFA World Cup – is believed to have been carried out by a male suicide bomber, which, officials said, probably worked with the same organisation behind an explosion at the city’s train station a day earlier.
“It is now possible to preliminarily say that the explosive device was set off by a suicide bomber – a man whose body fragments have been collected and sent for genetic testing,” the Federal Investigative Committee said in a statement.
The two explosions over the last two days have left more than 30 dead in Volgograd, which is located 400 miles northeast of the Winter Olympic and Paralympic host city, Sochi, with just 39 days to go to the Opening Ceremony.
Bach told insidethegames that he has personally written to Russia’s President Vladimir Putin to express his condolences and “confidence in the Russian authorities to deliver a safe and secure Games in Sochi”.
“This is a despicable attack on innocent people and the entire Olympic Movement joins me in utterly condemning this cowardly act,” he added.
“Our thoughts are with the loved ones of the victims.
“I am certain that everything will be done to ensure the security of the athletes and all the participants of the Olympic Games.
“Sadly terrorism is a global disease but it must never be allowed to triumph.
“The Olympic Games are about bringing people from all backgrounds and beliefs together to overcome our differences in a peaceful way.
“The many messages of support and solidarity from the international community make me confident that this message will also be delivered by the Olympic Winter Games in Sochi.”
The terrorist attacks do, however, raise concerns over Russia’s vulnerability to militant attacks during the Games and highlight the threat posed by the nation’s North Caucasus regions, such as Dagestan and Chechnya, where insurgents have been seeking an Islamic state, but Sochi 2014 has insisted it is confident of a “safe” event.
“Security and safety at Sochi 2014 has always been and will remain of paramount importance with an unprecedented level of planning and measures put in place over the last seven years,” a Sochi 2014 spokesman told insidethegames.
“Games security is being managed by the authorities in a highly rigorous way.
“We are confident the Games in Sochi are going to be safe and comfortable for all.”
Putin has also ramped up defence efforts, issuing instructions to a counterterrorism committee and law enforcement agencies “to strengthen security Russia-wide and specifically in the Volgograd region”, after the deadly bombings.
Meanwhile, the British Olympic Association (BOA) has said it is “monitoring the situation in Volgograd closely” as it remains in communication with the Foreign and Commonwealth Office, Metropolitan Police and IOC.
“For the British Olympic Association, we have no higher priority than the safety and security of our delegation,” read a statement from the National Olympic Committee.
“This is the case for every Games in which we participate – Summer, Winter, Continental and Youth.
“Our preparations for the Sochi 2014 Olympic Winter Games continue and we are confident the Russian officials will regularly assess the security measures that are in place to make certain the environment is as safe as possible.”
The Governor of Volgograd has declared three days of official mourning on January 1 until 3.
Contact the writer of this story at emily.goddard@insidethegames.