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Authorities have not made public details on those held after Sunday's attacks. But a police source told AFP the 13 were detained at two locations in and around Colombo.
The source said the 13 men are from the same radical group.
At least two of the eight attacks were carried out by suicide bombers, according to police and other sources, and three police were killed when another suicide bomber detonated explosives during a raid on a house where suspects were.