Foreign Minister Alexander Saltanov said on Friday the incident risked hurting relations between the two countries.
"Our main objective today is to obtain the freedom of our embassy staff and their return home," Deputy Foreign Minister Alexander Saltanov told a press conference on Friday.
"It's in the interests not only of the two men, but of Qatar and Russia and their bilateral relations," he added.
Qatar's interior ministry announced on Thursday two men had been charged with assassinating former Chechen president Zelimkhan Yandarbiyev.
A third Russian security agent was arrested and subsequently freed, according to Moscow.
The Russian foreign ministry on Friday summoned Qatar's ambassador to Moscow to hear Russia's protests about the arrests for the second time in two days.
Former Chechen president
Yandarbiyev was killed in his car
Russia's acting foreign minister Igor Ivanov angrily denounced the security agents' arrest on Thursday, complaining they had been detained by force without informing the Russian
embassy in Qatar.
Russia has flatly denied the accusations against the detained men and insisted it was not involved in the Chechen rebel figure's assassination.
Yandarbiyev briefly headed Russia's war-torn separatist republic of Chechnya in the mid 1990s.
The pair have been held for nine days, according to Saltanov, who said he was "worried for their health and their lives."
Saltanov said the two secret agents had been posted to the Russian embassy in Qatar to help in the "fight against terrorism," in particular terrorist financing.
The 51-year-old Yandarbiyev, who had lived in Qatar "temporarily" for nearly three years with his family despite a Russian extradition request.
Although never formally accused, Russia's SVR foreign intelligence service has said it has nothing to do with the death of Yandarbiyev, who was killed when his car blew up on 13 February.