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With the Czechs' hopes of qualification for World Cup 2014 all but over, coach Michal Bilek resigned after September's loss to Italy and interim boss Josef Pesice agreed to try other players.
"Arsenal have asked us to excuse Rosicky for health reasons. We have called up Borek Dockal," Pesice told the press.
National team director and former Liverpool star Vladimir Smicer explained: "Tomas wasn't completely fit after the [West Brom] game. Arsene Wenger got in touch with me and we agreed not to take Tomas to the qualifiers."
The 33-year-old Rosicky has 93 international caps to his name, having made his debut in 2000, and has scored 21 goals for his country.