State broadcaster TRT aired a video tape seized in the operation, said to be shot in Afghanistan, in which militants demonstrate the making of a bomb.
Most of the suspects -- 11 people -- were detained in the southern province of Gaziantep where the security forces, backed by armored vehicles, raided 11 locations in two districts, Anatolia said.
Four people were detained in the neighboring provinces of Şanlıurfa and Adana, and two others in the central city of Konya. They were to be brought to Gaziantep for questioning.
In a related operation in Kahramanmaraş, which also borders Gaziantep, police rounded up 17 alleged members of an unnamed group with suspected links to al Qaeda and continued to look for three others, Anatolia said. A newspaper reported in March that Ankara had received U.S. intelligence that al Qaeda militants could be plotting attacks on foreign targets in Turkey.
Following questioning by police, the suspects are to appear before courts, which will decide whether there is enough evidence to bring formal charges against them. The raids follow the arrest earlier this month of seven people accused of having links to al Qaeda, in simultaneous operations in the western province of Eskişehir. A Turkish cell of al Qaeda was held responsible for truck bombs against two synagogues, the British consulate and a British bank in Istanbul in 2003, which killed 63 people, including the British consul, and left many injured.