The Moldovan National Anti-Corruption Agency questioned the 12 following the conclusion of the clash between Dacia Chisinau and Dinamo-Auto Tiraspol, the MFF confirmed on Saturday.
Two people were arrested on Saturday in connection with alleged match fixing, according to local media reports but that remained unconfirmed by the Moldovan Federation.
"Twelve people from both clubs were held on Friday at around five in the evening," MFF spokesman Victor Daghi confirmed to Reuters.
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"We have not received any official information from the Moldovan National Anti-Corruption Agency and are waiting for it on Monday.
"It is possible that we may set up an official committee to investigate these claims."
The questioning came after former Moldovan champions and current league leaders Dacia had beaten Dinamo-Auto, currently bottom of the country's top division, 6-2.
Among those questioned were seven Dinamo-Auto players and the team's head coach, 35-year-old Igor Negrescu as well as Dacia's vice-president Ruslan Kmit and sporting director Muhajir Polonkoev.
Dinamo-Auto, who confirmed they had eight players and officials questioned, have complained that the move was illegal.
"After the match, armed members of the Moldovan National Anti-Corruption Agency came into our dressing room," the club said on their website (www.dinamo-auto.com).
"Without any explanation and without any reasoning, eight members of Dinamo-Auto were apprehended (seven players and a coach) in Chisinau where they were taken for questioning.
"Dinamo-Auto have sent an official letter to the Director of the Moldovan National Anti-Corruption Agency, Viorel Chetraru, to explain why this has happened."
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