* Trolleybus bombing follows Sunday's railway station attack
* Bombings underscore risks ahead of Sochi Games
* Moscow calls for international solidarity
* More attacks can be expected, says anti-terrorism expert (Adds police measures in Volgograd, report on identity of station bomber, quotes, U.S., British and IOC comment)
By Maria Tsvetkova
VOLGOGRAD, Russia, Dec 30 (Reuters) - A bomb ripped a bus apart in Volgograd on Monday, killing 14 people in the second deadly attack blamed on suicide bombers in the southern Russian city in 24 hours and raising fears of Islamist attacks on the Winter Olympics.
President Vladimir Putin, who has staked his prestige on February's Sochi Games and dismissed threats from Chechen and other Islamist militants in the nearby North Caucasus, ordered tighter security nationwide after the morning rush-hour blast.
The previous day's similar attack killed at least 17 in the main rail station of a city that serves as a gateway to the southern wedge of Russian territory bounded by the Black and Caspian Seas and the Caucasus mountains.
On Monday, the blue and white trolleybus - powered by overhead electric cables - was reduced to a twisted, gutted carcass. Bodies were strewn across the street as Russians prepared to celebrate New Year, the biggest annual holiday.
Windows in nearby apartments were blown out by the blast, which Russia's foreign ministry condemned as part of a global terrorist campaign.
"For the second day, we are dying. It's a nightmare," a woman near the scene told Reuters, her voice trembling as she choked back tears. "What are we supposed to do, just walk now?"
"Identical" shrapnel to that in the rail station indicated that the two bombs were linked, investigators said.
"There was smoke and people were lying in the street," said Olga, who works nearby. "The driver was thrown a long way. She was alive and moaning ... Her hands and clothes were bloody."
There was no immediate claim of responsibility for either of the two attacks. Investigators said they believed a male suicide bomber was responsible for Monday's blast. In Sunday's attack, the federal Investigative Committee initially described the bomber as a woman from Dagestan, a hub of Islamist militancy on the Caspian, but later said the attacker may have been a man.
Citing unnamed sources, the Interfax news agency said the suspected attacker in Sunday's blast was an ethnic Russian convert to Islam who had moved to Dagestan and joined militants there early in 2012.
Volgograd was also the scene of an attack in October, when a woman from Dagestan killed seven people in a suicide bus blast.
The violence raises fears of a concerted campaign before the Olympics, which start on Feb. 7 around Sochi, a resort on the Black Sea at the western end of the Caucasus range, 700 km (450 miles) southwest of Volgograd.
In an online video posted in July, the Chechen leader of insurgents who want to carve an Islamic state out of the swathe of mainly Muslim provinces south of Volgograd, urged militants to use "maximum force" to prevent the Games from going ahead.
"Terrorists in Volgograd aim to terrorise others around the world, making them stay away from the Sochi Olympics," said Dmitry Trenin, an analyst with the Moscow Carnegie Centre.
North Caucasus militants have also staged attacks in Moscow and other cities, the most recent in the capital being an airport suicide bombing three years ago that killed 37 people.
International Olympic Committee President Thomas Bach condemned the "despicable attack on innocent people" and said he had written to Putin to express condolences and confidence that Russia would deliver "safe and secure games in Sochi".
It was unclear why Volgograd has been hit, though it is close to the restive regions. It also has resonance in Russian national identity as the scene of the battle that turned the course of World War Two, when the city was known as Stalingrad.
Putin visited in February to mark the battle's 70th anniversary. City leaders have revived the old name for special occasions as Stalin's image has been somewhat rehabilitated under Putin, while Stalin remains a hate figure to Chechens, whose nation was deported en masse on his orders.
Putin has staked his personal reputation on a safe and successful Olympics. This month, he freed jailed opponents including oil tycoon Mikhail Khodorkovsky and the Pussy Riot punk band to remove causes for criticism at the event.
Intended to showcase how Russia has changed since the collapse of Soviet communism in 1991, the Games have also been a focus for complaints in the West and among Russian liberals that Putin has stifled dissent and encouraged intolerance.
Putin was first elected in 2000 after winning popularity for a war on Chechen rebels who had bid for independence after the break up of the Soviet Union. Attacks by Islamist militants whose insurgency is rooted in that war have clouded his 14 years in power and now present his biggest security challenge.
In a statement, the Foreign Ministry called on world powers to stand together against "terrorists" and named Doku Umarov, the Chechen warlord who leads the insurgency in the North Caucasus, as among those fomenting violence.
"We will continue our consistent fight against an insidious enemy that can only be stopped together," the ministry said.
Likening the Volgograd bombings to attacks in the United States, Syria, Afghanistan and elsewhere, it criticised those who seek to justify some such violence - an apparent dig at Western powers who have supported Syria's insurgents and who, at least in the 1990s, showed some sympathy for Chechen rebels.
"The United States stands in solidarity with the Russian people against terrorism," White House National Security Council spokeswoman Caitlin Hayden said. "The U.S. government has offered our full support to the Russian government in security preparations for the Sochi Olympic Games, and we would welcome the opportunity for closer cooperation for the safety of the athletes, spectators, and other participants."
Russia has in the past complained that Western countries do not consider its North Caucasus militants a threat, although Moscow cooperated with Washington after the Boston Marathon bombings that killed three people in April. The Boston suspects, two brothers, were Chechens who had lived in Dagestan.
On Twitter, British Prime Minister David Cameron said he was "shocked & saddened" by the attacks. "I've written to President Putin to say the UK will help Russia in whatever way we can."
Police said additional officers were deployed to railway stations and airports nationwide. In Volgograd province, more than 4,000 police and interior troops were activated in operation Anti-terror Whirlwind, checking documents and searching for suspicious people, Interfax quoted regional police as saying. Itar-Tass said they were focusing on migrant workers.
"There is a horrible feeling of helplessness against these monsters," said librarian Margarita Savicheva, 50. "I fear for my daughter, who also takes the trolleybus. Something diabolical has come to our town."
The police force in Volgograd, a city of a million people, has been depleted as some 600 officers were redeployed to Sochi to help with Olympics security a police officer told Reuters.
More attacks can be expected before the Olympics and nearby cities are easier targets than Sochi itself, said Alexei Filatov, a prominent former member of Russia's elite anti-terrorism force, Alfa.
"The threat is greatest now because it is when terrorists can make the biggest impression," he said. "The security measures were beefed up long ago around Sochi, so terrorists will strike instead in these nearby cities like Volgograd."
The attacks also threaten to fuel ethnic tension, which has increased with an influx of migrants from the poor Caucasus and Muslim Central Asian nations to Russian cities in recent years.
"They need to be chased out of here. It has become a transit junction - there are all these non-Russians, both good and bad," said Olga, a saleswoman at a store near the mangled bus.
Several dozen nationalists held a protest outside a chapel in the city on Monday and police detained more than 20 of them.
"We are Russian; we must not be afraid," said Mikhail Yasin, a protester who lit a candle for bombing victims. "God is with us. We are in our own land and no terrorist can frighten us - nor can the police." (Additional reporting by Alissa de Carbonnel; Writing by Steve Gutterman; Editing by John Stonestreet, Alastair Macdonald and Peter Graff)