The statement called the attack an "act of vengeance."
The Kurdistan Freedom Fighters is an offshoot of the Kurdistan Workers' Party (PKK). Turkey considers both groups to be terrorist organizations.
On Saturday night, two bombs exploded at a short interval near the Vodafone Arena Stadium killing 38 people.
"Unfortunately, the number of our citizens who died in the terrorist attack in Istanbul has reached 38 people, of which 30 are police officers. A total of 155 people are still being treated in hospitals," Turkish Interior Minister Suleyman Soylu said in a statement.
Tensions between Ankara and Turkish Kurds escalated in July 2015 when a ceasefire between Turkey and the PKK collapsed over a series of terrorist attacks, allegedly committed by PKK members.
