When contacted by AFP, the FSB refused to comment on the case immediately, saying it would respond to any written requests within 10 days.
Russian media have speculated that Moscow detained the Qataris in retaliation for Doha's arrest of two Russian security service agents, who are charged with assassinating former Chechen president Salim khan Yandarbiyev in the Qatari capital on 13 February.
Moscow's respected Kommersant daily on Thursday identified the two detained Qataris as Nasser Ibrahim Saad al-Madhihiki, an official with the Qatar Greco-Roman wrestling team and Ibad Akhmedov, an Azerbaijani who apparently has Qatar citizenship and competes for the team.
Qatari officials have identified the detainees as Nasser Ibrahim Saad al-Madhihiki and Ibrahim Ahmed Nasser Ahmed, members of the nation's wrestling federation.
The Qataris were detained on 26 February at Moscow's Sheremetevo airport where they stopped on a layover on their way to a competition in Serbia, according to Alexander Dubrovksy, the team trainer who was stopped along with the two men and later released.
"I told him, 'they're not terrorists, they're athletes,'... but he didn't believe me"
trainer, Qatar Wrestling Federation
The trio was detained when customs discovered that al-Madhihiki was carrying $7,200 that he did not declare, Kommersant quoted Dubrovsky as saying.
Dubrovsky said he was first interrogated by police and then by a plainclothes man who questioned him as to the identity of his two companions.
"He said 'they resemble composite sketches of terrorists who blew up the metro' (in early February)," Dubrovsky was quoted as saying. "I told him, 'they're not terrorists, they're athletes,'... but he didn't believe me."
Qatar's foreign ministry on Wednesday said Russia still had not provided it with any reasons for the arrests of the two men and has been denied contact with them despite repeated requests.
Airport police told Kommersant that "we don't have them, they're probably with the FSB."
The men were arrested shortly after Doha arrested two Russian security agents and charged them with orchestrating the car bombing that killed Yandarbiyev and injured his son.
Moscow has denied the agents had anything to do with the blast that killed the 51-year-old former Chechen president whom Russia suspects was raising funds for Chechen fighters abroad.
The blast that killed him came a week after an explosion ripped through a crowded Moscow subway train, killing at least 40 people, in the latest of a string of blasts in Russia ahead of presidential elections on 14 March.
Moscow has blamed Chechen fighters for the attacks.
Russian Defence Minister Sergei Ivanov, a former KGB officer, was quoted as saying on Wednesday that Moscow "would use all possible levers to free" its detained agents in Doha.