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The World Group second round showdown will then see Igor Andreev meeting Czech Radek Stepanek in Friday's second rubber.
The two countries have met twice after the fall of the Soviet Union in 1991 and the split of Czechoslovakia. Russia won both of their clashes in 1994 and 2003 3-2, however the two countries are still tied overall at 4-4.
For Saturday's doubles world number four Nikolay Davydenko has been named to play along with Mikhail Youzhny against Lukas Dlouhy and Pavel Vizner, who were named as the Czechs' doubles pairing by skipper Jaroslav Navratil.
"It will be a tough clash," Navratil said earlier this week. "I expect a long five-rubber battle just like our latest match in Ostrava in 2003."
Russian skipper Shamil Tarpishchev also said that both teams looked pretty even ahead of the start.
"We are very much alike. The Czechs are playing a similar style of tennis to us," Tarpishchev said. "It will be very important which team will adapt earlier and better to the courts here."
Reversed singles will complete the tie's schedule on Sunday.
The winner of this weekend's tie will face either Argentina or Sweden in a clash for a place in the final.
Draw for the Davis Cup World Group quarter-final tie which takes place here from Friday to Sunday:
Friday (0900 GMT start)
Marat Safin (RUS) v Tomas Berdych (CZE)
Igor Andreev (RUS) v Radek Stepanek (CZE)
Saturday (1000 GMT start)
Nikolay Davydenko/Mikhail Youzhny (RUS) v Lukas Dlouhy/Pavel Vizner (CZE)
Sunday (0900 GMT start)
Igor Andreev (RUS) v Tomas Berdych (CZE)
Marat Safin (RUS) v Radek Stepanek (CZE)
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