ISTANBUL — A Kurdish militant group claimed responsibility on Sunday for a double bombing that killed 39 people and wounded 154 outside a soccer stadium in the heart of Istanbul the night before.

The group — Kurdistan Freedom Falcons — said in a statement that two of its members had carried out the suicide attacks in retaliation for state violence in the predominantly Kurdish region in southeast Turkey. The group also cited the continuing imprisonment of Abdullah Ocalan, the leader of the Kurdistan Workers’ Party, or P.K.K., which has waged a three-decade insurgency against the Turkish state.

The Kurdish Freedom Falcons, which claimed responsibility in June for a car bombing in Istanbul that killed at least 11 people, is considered an offshoot of the Kurdistan Workers’ Party.