His son, Ramzan Kadyrov, is now the president of the Chechen Republic.
The spokesman for Chechen President Ramzan Kadyrov said the brothers had not been connected with the Chechen Republic for many years, Russia's semi-official Interfax news agency reported Friday.
In addition to appearing in commercials for Sovietsky Bank credit cards, Depardieu has friends in high places in the country, including the controversial head of the Chechen Republic, Ramzan Kadyrov.
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These attacks have been stepped up, especially after the Chechen people took part in the referendum, adopting the constitution of the Chechen Republic, which said that Chechnya is an integral part of the Russian Federation.
Russia insists that it is not going to talk to Mr Maskhadov, because he does not "control the situation" in the republic - a claim the Chechen president rejects.
The family was eventually forced to flee to the neighbouring Russian republic of Dagestan after the Second Chechen War broke out in 1999.
They are thought to have lived in Kyrgyzstan, a Central Asian republic which is home to many Chechen refugees who were deported under Stalin.
Interfax said that another 500 Russian soldiers had been dispatched to the Georgian-Chechen border in order to intercept any Chechen attempt to escape south into the former Soviet republic.
Though he is ethnically Chechen, Anzor Tsarnaev grew up in the former Soviet republic of Kyrgyzstan because his parents were deported there in the Stalin era alongside many other ethnic Chechens.
Chechen-led rebels, who are not backed by the republic's nominal government, have been able to move effortlessly between their home bases and neighbouring Dagestan, where they are trying to foment an uprising.
Hundreds of thousands of Estonians, Latvians, Lithuanians, and Poles were dispatched to the Gulag (most during the same timeframe as the Chechen deportation), and countries as varied as the Czech Republic, Slovakia, and Bulgaria were crushed beneath the Soviet jackboot for decades.
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As many as 7, 000 Chechen fighters are holed up in the rugged remote south of the republic, according to Moscow, where the inaccessible terrain allowed them to launch deadly counter-attacks against Russian forces in the 1994-96 war.
Everyone in the republic had memories of Stalin's deportation of the entire Chechen people in 1944.
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Meanwhile, it is understood that the ethnic Chechen suspects' father, Anzor Tsarnaev, has not yet left for the US from the Russian republic of Dagestan, despite earlier saying he would do so.
The ethnic Chechen family came to this country in 2002, after fleeing troubles in Kyrgyzstan and then Dagestan, a predominantly Muslim republic in Russia's North Caucasus.
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