MOSCOW (AFP) - At least 14 people were killed on Monday when a suicide bomber blew himself up on a packed trolleybus in Volgograd, raising new concerns about security at the Sochi Olympics a day after a deadly attack on the southern Russian city's train station.

President Vladimir Putin ordered stepped-up security across the country after the trolleybus bombing at the peak of the morning rush and Sunday's suicide attack blamed on a suspected female suicide bomber which claimed 17 lives.

The attacks on Volgograd, which until this year had no record of recent unrest, raised alarm about whether the ongoing anti-Kremlin insurgency in the Northern Caucasus could affect the Sochi Winter Games which open on February 7.

The force of Monday's blast destroyed the number 15A trolleybus, which was packed with early morning commuters and was turned into a tangle of wreckage with only its roof and front remaining.

Health ministry spokesman Oleg Salagai told Russian state television that 14 people were killed and 28 wounded.

Russian investigators have opened a criminal probe into a suspected act of terror as well as the illegal carrying of weapons, the Investigative Committee said.

"The explosives were detonated by a male suicide bomber, fragments of whose body have been found and taken for genetic analysis to establish his identity," said spokesman Vladimir Markin.

He said four kilograms of TNT equivalent had been used and noted that the explosives were identical to those used in Sunday's train station bombing.

"This confirms the theory that the two attacks are linked. It is possible that they were prepared in the same place," he added.

The United States called for closer security cooperation with Russia after the bombings, saying it had offered Russia its full support and warning Americans to stay vigilant.

National Security Council spokeswoman Caitlin Hayden said Washington "would welcome the opportunity for closer cooperation for the safety of the athletes, spectators, and other participants".

IOC head Thomas Bach condemned the attacks but said he was confident security would be solid at the Olympics.

"The Olympic Games are about bringing people from all backgrounds and beliefs together to overcome our differences in a peaceful way," he said.

UN leader Ban Ki Moon and the UN Security Council said they were "outraged" by the latest attack.

Putin has assured Ban "that Russia would work within the bounds of international law to bring the perpetrators to justice", said UN spokesman Martin Nesirky.

German Chancellor Angela Merkel also condemned the attacks.

Putin ordered security stepped up across Russia, with a special regime to be imposed in Volgograd, which lies 690 kilometres northeast of the Black Sea resort of Sochi, the national anti-terror committee announced.

Federal Security Service (FSB) chief Alexander Bortnikov flew to Volgograd and asked citizens to be understanding about the extra security that may involve spot checks.

"It is a necessary measure," he said.

Russia is already preparing to impose a "limited access" security cordon around Sochi from January 7 which will check all traffic and ban all non-resident cars from a wide area around the city.

The head of the Russian Olympic Committee, Alexander Zhukov, said there was no need for extra security measures in Sochi as "everything that is necessary has already been done", ITAR-TASS reported.

The search for the perpetrators is expected to focus on Russia's largely Muslim North Caucasus region where Islamist militants have for years been fighting the Russian security forces.

Doku Umarov, the leader of militants seeking to impose an Islamist state throughout North Caucasus, has ordered rebels to target civilians outside the region and disrupt the Games.

"This looks like the North Caucasus underground. They promised to stage acts in big Russian cities ahead of the Olympics. It seems they are fulfilling their promise," military affairs commentator Pavel Felgenhauer told AFP.

Moscow city hall's security chief Alexei Mayarov said precautions would be stepped up in the capital ahead of New Year, the biggest holiday of the year in Russia and traditionally marked by mass outdoor gatherings.

Reports said Russia's second city of Saint Petersburg had already cancelled its planned New Year fireworks display.

Militant strikes have become part of daily life in the North Caucasus. But the Volgograd blasts will be a particular concern to the authorities as the bomber struck a city of more than one million people in the Russian heartland.

The city, known as Stalingrad in the Soviet era, is of huge importance to Russians as the scene of one of the key battles of World War II that led to the defeat of invading Nazi forces.

The city was previously attacked on October 21 by a female suicide bomber with links to Islamists who killed six people on a crowded bus.

Russia's double Olympic pole vault champion Yelena Isinbayeva, Volgograd's best known current inhabitant, told ITAR-TASS she felt "terrible, simply terrible" after the attacks.

The blasts are the deadliest in Russia since a suicide bombing at Moscow's Domodedovo airport killed 37 people in January 2011.