MOSCOW (Reuters) - A suicide bomber killed at least 35 people at Russia’s busiest airport on Monday, state TV said, in an attack on the capital that bore the hallmarks of militants fighting for an Islamist state in the North Caucasus region.

President Dmitry Medvedev vowed to track down and punish those behind the bombing, which also injured over 150 people, during the busy late afternoon at Moscow’s Domodedovo airport. The dead included some foreigners.

Islamist rebels have vowed to take their bombing campaign from the North Caucasus to the Russian heartland in the year before presidential elections, hitting transport and economic targets. They have also leveled threats at the 2014 Winter Olympics, scheduled for the Black Sea resort town of Sochi, a region some militants consider “occupied.”

Dense smoke filled Domodedovo’s international arrivals hall and a fire burned along one wall.

“Taxi drivers lined up in the arrivals hall were blown up. Pieces of their bodies covered us and my left ear doesn’t hear very well at all,” Artyom Zhilenkov, 30, told Reuters as he pointed to pieces of human flesh on his coat.

Thick drops of blood were scattered across the snow-covered tarmac outside the arrivals hall, where Interfax news agency said traces of shrapnel were found.

Two Britons were among the dead, media cited investigative committee spokesman Vladimir Markin as saying, and French, Italians, and Germans were in hospitals, though this could not be immediately confirmed with their embassies. Planes from across Europe had landed in the half hour leading up to the attack.

“I heard a loud boom... we thought someone had just dropped something. But then I saw casualties being carried away,” a check-in attendant who gave her name as Elena told Reuters at Domodedovo, which is some 22 km (14 miles) southeast of Moscow.

The prosecutor’s office said the bomb had been classified as a terrorist attack -- the largest since twin suicide bombings on the Moscow metro rocked the Russian heartland in March.

“The blast was most likely carried out by a suicide bomber.”

State television said the blast was the work of a “smertnik,” or suicide bomber. State-run RIA, quoting Markin, said the bomber most likely had a belt laden with explosives.

U.S. President Barack Obama condemned the “outrageous act of terrorism” and offered Moscow help. NATO Secretary General Anders Fogh Rasmussen said he was shocked, state TV said.

A decade after federal forces drove separatists from power in Chechnya in the second of two wars, the mainly Muslim North Caucasus is wracked by violence.

Medvedev, who has called the Islamist insurgency in the North Caucasus the biggest threat to Russian security, wrote on Twitter: “Security will be strengthened at large transport hubs.”

“We mourn the victims of the terrorist attack at Domodedovo airport. The organizers will be tracked down and punished.”

Medvedev, due to open the World Economic Forum on Wednesday, delayed his Tuesday departure to the Swiss city of Davos.

No group has yet taken responsibility for the attack, but dozens of Internet surfers, writing in Russian, praised the suicide bomber on unofficial Islamist site kavkazcenter.com.

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Russia’s rouble-denominated stock market MICEX fell by nearly two percent following the blast, but traders said they expected little long-term impact.

“It (the blast) is moving the market in the short term, but there is no fundamental reason for the market to fall. If you remember, the market didn’t react strongly to (previous blasts),” said trader Alexei Bachurin from Renaissance Capital.

However, analysts and insiders could change their tune if Russia sees a sustained a wave of such attacks, which could dent its $1.2 trillion economy, which is recovering from the global crisis.

The attack raised questions over Russian security -- one month after it won the right to host the 2018 World Cup.

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SPREADING INSURRECTION

Twitter users posted mobile video phone footage of dozens of people lying on the floor amongst severed limbs and pools of blood as thick smoke filled the hall.

Airport staff were shown using flash lights to pick their way through the chaotic scene taped off immediately after the blast. Later videos showed emergency workers wheeling injured people out of the terminal on stretchers.

Prime Minister Vladimir Putin, who shares power in a ‘tandem’ arrangement with the less influential Medvedev, has staked his political reputation on quelling rebellion in the North Caucasus.

He launched a war in late 1999 in Chechnya to topple a secessionist government. That campaign achieved its immediate aim and helped him to the presidency months later; but since then insurgency has spread to neighboring Ingushetia and Dagestan.

“It does not ... bode well for Russian ties to the North Caucasus and is yet another sign that what Putin started in 1999 by invading the rebellious republic of Chechnya has come home to roost again in the Russian capital,” said Glen Howard, president of the U.S. Jamestown Foundation research institution.

Tensions between ethnic Russians and Muslims -- at 20 million they make up one seventh of Russia’s population -- flared dramatically last month in a string of clashes, which involved thousands of Russian nationalists who attacked passersby of non-Slavic appearance, many of whom were from the North Caucasus.

Analysts say rebels are planning to increase violence in the run up to 2012 presidential elections, that may well see Putin returning to the presidency.

“It is a clear jab at the FSB (Federal Security Services) and at the elections,” said Adil Mukashev, an independent expert on terrorism issues.

Security has been tightened at Moscow’s other two airports, which will also receive diverted passengers who were flying toward Domodedovo, media reported.

Moscow suffered its worst attack in six years in March 2010 when two female suicide bombers from Dagestan set off explosives in the metro, killing 40 people.

The worst incident involving North Caucasus rebels took place in 2004 when militants seized control of a school in Beslan. When Russian troops stormed the building in an attempt to end a siege, 331 hostages, half of them children, were killed.