The agency, citing police, said that the suspects were rounded up for questioning in simultaneous raids in the cities of Bursa and Istanbul earlier this week and on Thursday. It did not elaborate.
It was the latest in a string of raids against people described as al-Qaida suspects. The suspects were expected to be interrogated by prosecutors on Friday who will decide whether to press charges against them.
Some charges emerging from similar previous raids have been dropped because of flimsy evidence.
Islamic militants tied to al-Qaida carried out suicide bombings in Istanbul in 2003, killing 58 people.
In 2008, an attack blamed on al-Qaida-affiliated militants outside the U.S. Consulate in Istanbul left three attackers and three policemen dead.