Russian forces are on high alert over threats by Islamist militant groups based in the nearby north Caucasus to attack the Winter Games, which offcially begin today. Twin suicide bombings killed at least 34 people in December in Volgograd, some 400 miles north-east of Sochi.
Deputy Prime Minister Dmitry Kozak, speaking on the eve of the opening ceremony, said Russian security services were working with colleagues from Europe and North America.
He added: "There is no reason to believe the level of danger in Sochi is greater than at any other point on the planet, be it Boston, London, New York or Washington. We can guarantee the safety of people as well as any other government hosting any mass event."
President Vladimir Putin, who launched a war to crush a rebellion in nearby Chechnya in 1999, has staked his reputation on the Games, which at around £30 billion will be the most expensive in Olympic history.
Islamist guerrillas seeking an independent Islamic state in Chechnya and neighbouring regions of southern Russia have aimed threats at the games, which they argue take place on land seized from Caucasus tribes in the 19th century.
Despite a ring of steel around venues and some 37,000 security personnel on alert, Russia fears a woman suspected of planning a suicide bombing may have slipped through. Her details were circulated last week.
However, security officials believe the risk of an attack is far greater elsewhere in Russia than in Sochi.
President Barack Obama has said he believed Sochi was safe but behind the scenes there has been tension between Russian and US officials, including over concerns the host nation might react with excessive force in the case of an attack and endanger civilian lives.