Presiding judge Ibrahim Salah al-Nisf ordered the hearings to be held behind closed doors on Sunday at the request of the defence lawyer and "given the nature of the trial".
The court has begun hearing the testimony of 13 prosecution witnesses.
Two witnesses took the stand at morning and afternoon sessions, and two more were due to testify when the hearing resumes on Monday, the source said.
The widow and other members of the family of Zelimkhan Yandarbiyev, who was living in exile in Doha when he was assassinated on 13 February, were in court.
"I have come to see the faces of the men who killed my husband," Malika Yandarbiyev told reporters, adding that she would have preferred the hearings to be "open to the public".
The trial of Anatoly Bilashkov and Vassily Pokchov on 10 charges, including the murder of Yandarbiyev, opened on 11 April.
They are also accused of attempting to kill Yandarbiyev's 13-year-old son and of smuggling arms into Qatar, according to the charge sheet read out in court by a representative of the prosecutor general.
"I have come to see the faces of the men who killed my husband"
The first defendant has pleaded not guilty to all charges but the second has pleaded guilty to a secondary charge of "deception and forgery".
Quoting confessions by the accused, the representative said: "The arms used in the killing came via the Saudi-Qatari border in a diplomatic car."
A Russian defence lawyer was quoted by the Interfax news agency as claiming the confessions were extracted under duress.
In what escalated into a diplomatic row between the Gulf state and Russia, Qatar expelled the first secretary of the Russian embassy late last month after detaining him and the agents in connection with the murder of Yandarbiyev in a car bombing.
Yandarbiyev was killed in a car
bomb after leaving prayers
The announcement of the expulsion was made just hours after the return to Doha of two Qatari nationals who were released by Moscow.
The two members of the Gulf state's wrestling federation were arrested in transit at Moscow's Sheremetyevo airport on 26 February on suspicion of carrying undeclared foreign currency in what was seen as a tit-for-tat move.
But during a visit to Doha on 18 April, Russian Security Council chief Igor Ivanov said Moscow would respect the Qatari courts' ruling in the case.
Russia has demanded that Qatar free the two agents, saying they had nothing to do with Yandarbiyev's murder.
Moscow's SVR foreign intelligence service also said it had nothing to do with the death of Yandarbiyev, who briefly headed Russia's war-torn separatist republic of Chechnya in the mid-1990s.
Yandarbiyev, who had lived in Qatar for nearly three years with his family despite a Russian extradition request, was accused by Moscow of raising funds for Chechen rebels.