Captain Eduard Ulman and three other servicemen have been accused of attacking a vehicle and killing its driver and passengers during a reconnaissance raid in the troubled North Caucasus republic in January 2002.
The judge ordered Ulman, Voyevodin, and Kalagansky into custody after they failed to show up in court.
Their defense lawyer said he had been unable to get in touch with them.
The judge did not impose a restraining order on the fourth defendant, Alexei Perelevsky, who appeared in court.
The court adjourned till May 24.
The defendants earlier admitted involvement, but denied the charges against them. North Caucasus Military Court juries twice acquitted Ulman, Perelevsky, Lieutenant Alexander Kalagansky and Warrant Officer Vladimir Voyevodin on charges of murder and abuse of office.
But the Supreme Court upheld an appeal filed by prosecutors and backed by lawyers acting for the victims, and ruled that a professional non-jury court should hear the case.
The Constitutional Court ruled last year that serious crimes committed in Chechnya could be tried without a jury. The ruling came following an inquiry made by then-Chechen President Alu Alkhanov concerning the legality of several articles in the laws on military courts that he said gave the military rights not enjoyed by ordinary citizens.