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Under interrogation, the men also told the Qataris that the bomb used to kill Zelimkhan Yandarbiyev last month was smuggled into the tiny Gulf state after being sent from Moscow through the diplomatic bag into Saudi Arabia.
Qatar has promised to put the two men on trial but has come under enormous pressure from Russia to release them instead.
Moscow would be hugely embarrassed by any trial if it revealed that its agents were instructed to assassinate Mr Yandarbiyev, and even more so if it were shown that the bomb had been brought in through the diplomatic bag. Russia’s appeal for joint international action against Chechen terrorism would be severely compromised as a result.
So desperate is the Kremlin to forestall any trial that it is understood to have threatened to send special forces to mount an operation to spring the men from prison and take them back to Russia.
Pressure on Qatar has also been increased by the arrest of two Qatari citizens who are being held by the FSB security service in Russia.
The two men have been identified as Nasser Ibrahim Saad al-Madhihiki, an official with the Qatari greco-roman wrestling team, and Ibrahim Ahmad Nasser Ahmad. A third man, Ibad Akhmedov, is a Belarussian who apparently has Qatari citizenship and was detained at the Sheremetyevo-2 international airport in Moscow but later released.
The Russians are clearly hoping to swap the two men for the detained security officials held in Qatar.
The Qataris appear embarrassed by the affair, and have refused to comment further on the case. But Western diplomats say that the authorities appear determined to go ahead with a trial.
The Qataris have been outraged by the killing of Mr Yandarbiyev, whom the Russians hold responsible for masterminding the Moscow theatre siege which killed around 120 hostages and several Chechen rebels on 23 October, 2002.
Most victims died after Russian special forces stormed the building to free about 800 people who had been held hostage for more than two days.
Mr Yandarbiyev briefly took over as Chechen president in 1996 after the death of Dzhokhar Dudayev in an explosion. He was also seen as a key figure behind the 1999 incursion by Chechen rebels into the neighbouring Russian region of Dagestan.
A Russian Foreign Ministry official yesterday denied that there had been an escalation of the dispute between Russia and Qatar. He told The Times: “I haven’t heard of any such threatening language.”
A spokesman for the FSB, the KGB’s successor, declined to comment yesterday. But this month Sergei Ivanov, Russia’s Defence Minister, made it clear that Russia would do everything in its power to get its detained citizens back.
He told reporters in Paris: “The State will use all available instruments to release the Russian citizens illegally detained in Qatar.”
Mr Ivanov did not elaborate, but last October he announced that Moscow would use preventive military force in case of a “direct threat” to Russian citizens. Sergei Lavrov,Russia’s new Foreign Minister, said on Wednesday that Moscow’s position remained unchanged.
“We are expecting an appropriate response from Qatar. No evidence has been received so far proving the guilt of these two Russian citizens,” he said.
The dispute has fanned conspiracy theories and nationalist rhetoric in the run-up to the presidential elections in Russia on Sunday.
Some media reports have suggested that the security services had the tacit approval of the CIA to assassinate Mr Yandarbiyev. Others have accused the CIA of tipping off Qatari Intelligence about Russian involvement in the killing.
Dmitry Rogozin, co-leader of the nationalist Rodina bloc, and deputy Speaker of parliament, has called openly for the use of military force to persuade Qatar to free the Russian agents.
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