Mr. Kosachyov commented on a recent statement by Steven Pifer, US Under-secretary of State for Europe and Eurasia, in which he admitted that Washington had provided technical assistance to Qatar in arresting the Russian nationals on suspicion of involvement in the assassination of Zelimkhan Yandarbiyev, a Chechen separatist leader.
"It is deplorable that the US, which had recently advanced the initiative that Mr. Yandarbiyev should be put on the list of the most dangerous terrorists of the world, compiled by the UN, did not provide technological and political assistance to the international community, when it was searching for this international terrorist," said Mr Kosachyov.
No evidence of the Russian nationals' involvement in the assassination of Mr. Yandarbiyev has been furnished, noted the MP.
The chairman of a related Duma committee criticised the Qatari authorities for not allowing the arrestees to meet their lawyers.
Three Russian security officers were arrested in Qatar on February 18 on charges of being part of the assassination of Mr. Yandarbiyev. One of the arrestees, who had a diplomatic passport, was released later.
The Russian Foreign Ministry issued a statement in the wake of the arrest, saying the officers were staying in Qatar legally and were gathering and analysing information as part of an anti-terrorist effort and did not violate Qatari law.
The Russians continue to be jailed, and the local authorities insist they should be brought to trial.
Russian Foreign Minister Sergei Lavrov said last week that Moscow demanded that the arrestees should be allowed to return home.
"Russia's position (on the arrest) was set out by ex-Foreign Minister Igor Ivanov. It has not changed since then. We have appealed to the Qatari authorities insisting that the Russian nationals should be allowed to return to Russia," said Mr. Lavrov.