Sources in the ministry report that the ambassador met Russian Deputy Foreign Minister Alexander Saltanov.
Qatar's embassy in Moscow declined to comment on the meeting.
Three Russian nationals, who were on a business trip to the country and were staying at the Russian embassy, were arrested in Doha, Qatar's capital, in the early hours of February 19. One of the arrestees, who enjoys diplomatic immunity, was released later.
The Russian nationals are accused of involvement in the assassination of ex-Chechen president Zelimkhan Yandarbiyev, who had lived in Qatar for the last four years as an honorary guest of Qatar's Emir, Sheikh al-Thani.
Russian acting Foreign Minister Igor Ivanov issued a statement, saying the arrest was made by brute force. The Qatar authorities did not even notify the Russian embassy of the arrest, which runs counter to the "basic norms of inter-state relations." Moreover, the arrestees were denied a meeting with Russian embassy officials for 7 days, reads the statement.
Mr Ivanov said the arrested Russian citizens, one of whom held a diplomatic passport, were security officers.
"Their sojourn in Qatar was legal, they were gathering and analyzing information as part of an anti-terrorist effort. Their actions fall in line with the international anti-terrorism coalition's efforts to trace financial sources and channels, organizational arrangements and other means of support for terrorist organizations," Mr Ivanov said in the statement.
"The Russian government is taking measures to protect its nationals. The acting foreign minister has sent a special envoy to Doha for talks with the authorities. One of the arrestees was, thereby, released and he is staying at the Russian embassy now. Further efforts are being made to have the other two arrestees freed. The Qatar authorities are responsible for the life and health of the illegally imprisons Russian nationals," emphasizes the statement.