(CNN) -- A claim of responsibility that emerged Sunday for last month's back-to-back bombings in the Russian city of Volgograd also threatens "a present" for visitors to the upcoming Winter Olympic Games in Sochi.
In a video posted on a well-known Jihadi forum website Sunday, two young men believed to have been suicide bombers speak of the Volgograd attacks and also make an ominous promise.
"We've prepared a present for you and all tourists who'll come over. If you will hold the Olympics, you'll get a present from us for the Muslim blood that's been spilled," the video says.
In the video, the men are dressed in black and standing in front of a black banner with religious verse that is typically associated with al Qaeda-linked extremists.
Last month's attacks in Volgograd, a major transit hub about 650 kilometers (400 miles) away from Sochi, sparked concerns over security as the Olympics approach. The explosions targeted a train station and a trolley bus and claimed the lives of more than 30 people.
The fresh claim of responsibility came on the same day that Russian President Vladimir Putin pledged that visitors to Sochi for the Winter Olympics, due to start in less than three weeks, will be kept safe.
A transcript of his interview with half a dozen national and international broadcasters was posted on the Kremlin website Sunday.
"We will try to make certain that the security measures are not intrusive or too conspicuous, so they are not too noticeable for the athletes, the Olympics' guests or journalists," Putin said.
"But at the same time, we will do our utmost to ensure that they are effective."
Russia has plenty of experience in keeping international events secure, Putin said, pointing to the G8 and G20 summits as examples.
"Security is to be ensured by some 40,000 law enforcement and special services officers," he said. "Of course, we will draw on the experience acquired during similar events held in other regions of the world and in other countries. It means that we will protect our air and sea space, as well as the mountain cluster."
In addition to the Volgograd attacks, there has also been violence in recent days in the southern republic of Dagestan -- the latest unrest linked to a long-running Islamist insurgency in the North Caucasus region.
Putin acknowledged that the games, like any high-profile event, would be a target for terrorists.
But, he said, Russia has a "perfect understanding" of the threat and how to stop it.
'No danger' for gay visitors
Russia's stance on gay rights has been another area of concern for many visitors ahead of the games.
Russia has come under international pressure since its parliament passed a law last summer outlawing "gay propaganda." The legislation makes it illegal to tell children about gay equality and has been widely criticized by Western leaders, who have called it archaic and discriminatory.
But Putin defended it before journalists Friday, saying that the law was about protecting children.
"We have just recently passed a law prohibiting propaganda, and not of homosexuality, but of homosexuality and child abuse, child sexual abuse. But this has nothing to do with persecuting individuals for their sexual orientation," he said.
"So there is no danger for people of such nontraditional sexual orientation who are planning to come to the Games as guests or participants."
There has also been criticism of Russia over the limitations placed on freedom of speech at Sochi. The official protest site is about a 30-minute drive from the Olympic village and is difficult to find.
But Putin said no visitors should fear problems if they protest, for example, over gay rights.
Putin: No corruption
The Russian leader also dismissed claims that corruption has pushed up the cost of the games, saying there was no proof that had occurred.
When it won the bid in 2007, Russia said the Winter Games would cost $12 billion -- but the government's website now cites the total cost as 1.5 trillion rubles ($45 billion.)
"I do not see serious corruption instances for the moment, but there is a problem with overestimation of construction volumes," Putin said.
He suggested the problem was a universal one, where companies underestimate costs in the tendering process in order to win the project, and then push the price back up.
But, he said, there was no evidence of anything that could be considered corruption, or "theft of public funds with the help of state officials in whose hands these funds fall," in Sochi.
"If anyone has such information, give it to us, please. I repeat once again, we will be grateful. But so far there was nothing but talks," he said.
Putin put the cost of preparations for the Winter Olympics at only 214 billion rubles ($6.4 billion) -- but acknowledged that the total sum including the cost of major infrastructure projects was much higher.
The total price tag of $45 billion outstrips the $40 billion China is thought to have spent on the Beijing Summer Games and is more than three times the cost of London 2012.
Boris Nemtsov, former deputy prime minister of Russia and a vocal critic of Putin, published a report last year describing the Sochi games as one of the most "outrageous swindles" in recent Russian history. He claimed that up to 60% of the final cost -- or $30 billion -- has been embezzled.
CNN's Nic Robertson in Sochi and Virginia Harrison in London contributed to this report.
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