Hands clad in red gloves fiddle with powder and equipment as they prepare what are apparently explosive devices. Then, two men clutching machine guns speak to the camera and promise that the Olympics will involve "a present for all the innocent Muslim blood being spilled around the world".

The chilling video, posted on Sunday on the website of the Caucasus-based militant group Vilayat Dagestan, has renewed security fears ahead of the Sochi Olympics, which begin in 18 days. "For the tourists who come, there will be a present too," says one of the men. The video claims that the men were the two suicide bombers responsible for twin blasts that killed 34 people in the city of Volgograd at the end of December.

There was no confirmation of this, and Russian security officials did not comment on the video, which comes as US officials went public with their concerns about the level of intelligence sharing ahead of the games.

The US military said on Monday that air and naval assets, including two ships in the Black Sea, would be made available to help Russia combat any possible terrorist attack. "The United States has offered its full support to the Russian government as it conducts security preparations for the Winter Olympics," Pentagon spokesman Rear Admiral John Kirby said in a statement reported by Reuters.

"Air and naval assets, to include two navy ships in the Black Sea, will be available if requested for all manner of contingencies in support of – and in consultation with – the Russian government."

US officials acknowledge, however, that the likelihood of Russia asking the US for help would be low.

Privately, Russian officials admit that the security threat is high and that there could be attacks in other Russian cities during the games, but believe that the "ring of steel" operation to secure Sochi makes an attack there extremely unlikely during the Olympics. Security will be provided by a mix of police, special forces, security agents, the army and Cossack volunteer patrols.

In an interview with foreign TV networks over the weekend, President Vladimir Putin said the security would be extensive but low visibility: "Security is to be ensured by some 40,000 law enforcement and special services officers … We will protect our air and sea space, as well as the mountain cluster. I hope things will be organised in such a way that they don't catch the eye and, as I have already said, will not, so to say, depress the participants in the Olympic Games."

The new video threat follows reports that Doku Umarov, self-styled "emir" of the North Caucasus terrorist movement, has been killed by Russian security forces. Umarov had promised attacks on the Olympics and the Russians have long wanted him dead.

"Journalists have been asking me whether Doku Umarov presents a threat to the Olympics in Sochi," said Ramzan Kadyrov, the Kremlin-backed ruler of Chechnya, last week. "I have said before that he is dead, and we have now received a recording of some so-called 'emirs' [terrorist leaders], where they are discussing his death and consoling each other, and thinking about who to make the new head. They have more to worry about than the Olympics. So all the talk of a threat to the Olympics is absolutely unfounded."

However, even if Umarov really is dead, it is unclear how much day-to-day control he had over the terrorist movement, which carries out frequent attacks on officials in the North Caucasus but has struggled to carry out large-scale attacks in Russia in recent years. Security experts suggest there are a large number of terrorist cells operating more or less independently across the Caucasus region.

Russian special forces during an operation against suspected Islamic militants in Russia's North Caucasus territory of Dagestan. Photograph: Reuters

The Volgograd bombings showed that the potential is still there to strike at Russia's heartland, and in recent days there have also been reports of a female suicide bomber on the loose in Sochi, with hotel staff handed photographs of a woman in a pink headscarf who is believed to be planning a suicide attack.

Mark Galeotti, a Russian security expert at New York University, said the Olympics were a matter of prestige for the terrorist underground as well as for Putin – who on Monday received a boost with the news that the Chinese president, Xi Jinping, will attend the opening ceremony, unlike some other world leaders.

"[Terrorists] are haemorrhaging people to Syria and are in a battle for funding and support globally. Additionally, the regional groupings are battling for support with each other. They will really want to try to make an impact."

Nevertheless, he said, while the Russian prevention tactics have hardly been subtle, they may well work due to the sheer amount of resources used: "The Russians have played to their strengths. They have been going from door to door doing raids across the North Caucasus. It is not very precise, but the key tactic is to keep the terrorists busy trying to avoid being caught or shot, and thus too busy to plan anything during the Olympics."

Andrei Soldatov, an investigative journalist specialising in the Russian security services, said that the heavy-handed approach had its weaknesses, however: "There is a reliance on an entirely military response, and a weakness in intelligence gathering and informants."

The government has ended an amnesty programme that allowed insurgents not involved in serious terror attacks to be "rehabilitated" and provided rich sources of intelligence. It also introduced tough laws that could see property confiscated from terrorists' relatives. "The relatives of terrorists are exactly the people who should be the best source of intelligence," said Soldatov.

The British Olympic Association has confirmed that it will include specific security staff in its delegation to Sochi, amid heightened concern about the safety of athletes. However, a BOA spokesman stressed that security officers had been part of the British delegation in some form at every Olympics since Athens in 2004.

"We will have security personnel as part of our delegation. That's not new, it's something we've done for every Olympics at least since Athens. We stay in regular communication with the FCO [Foreign and Commonwealth Office] and the Metropolitan police. That is standard practice for us and those lines of communication remain open," said a spokesman.

Co-operation between the British and Russian security services was suspended in the wake of Alexander Litvinenko's murder with polonium in London in 2006, but when David Cameron visited Putin in Sochi last year, the pair said that intelligence sharing would be renewed before the Olympics.

A source involved in the Games' security planning suggested relations between security services in the US, Britain and Russia had not only been "thawed" but had been "put in the microwave" in the runup to the Games in an attempt to share intelligence and ensure the safety of the 6,000 competitors and tens of thousands of spectators.

However, US security officials have sounded less confident about the Russian preparations and level of intelligence sharing. Michael Morell, former deputy director of the CIA, said that the usual pre-Olympic intelligence sharing had simply not happened with the Russians: "I think fundamentally they don't want to admit that they don't have complete control here and they might need some help," he told CBS.