Defence lawyer Muhsin al-Suwaidi said Anatoly Bilashkov and Vassily Pokchov would appear before the prosecutor general on 8 June.
Both are charged with murdering Salim Khan Yandarbiyev, attempting to murder his 12-year-old son and smuggling arms into Qatar.
Anatoly has pleaded not guilty to the 13 February assassination of the retired Chechen official living in exile.
The closed-door trial began in Doha on 11 April and 13 prosecution witnesses have been heard to date.
The murder sparked a diplomatic row between the Gulf state and Russia.
Qatar expelled the first secretary of the Russian embassy in March after detaining him along with the agents in connection with the car bombing.
The expulsion announcement came just hours after the return to Doha of two Qatari nationals arrested by Moscow in what was seen as a tit-for-tat move.
Yandarbiyev fled Chechnya in
1998 and chose to live in exile
Russia has insisted the two agents had nothing to do with the bombing and Moscow's SVR foreign intelligence service also denied involvement.
Yandarbiyev, who briefly headed Russia's war-torn separatist republic of Chechnya in the mid-1990s, had lived in Qatar for nearly three years with his family.