The Kurdish militant group TAK says it carried out Saturday's deadly attack on police outside a stadium in Istanbul.
The TAK, an offshoot of the banned Kurdistan Workers' Party (PKK), made the claim on its website.
At least 38 people died near the Vodafone Arena when a car bomb hit a police vehicle and a suicide bomber blew himself up nearby after a top-division football match.
The TAK has said it was behind other deadly attacks in Turkey this year.
In Sunday's statement, it said the latest bombings were in reprisal for ongoing violence in the south-eastern Turkey and for the continuing imprisonment of PKK leader Abdullah Ocalan.
Earlier on Sunday, Deputy Prime Minister Numan Kurtulmus said initial findings pointed towards the PKK.
The BBC's Mark Lowen in Istanbul says many Turks believe the Kurdistan Freedom Falcons (TAK) are the PKK under a different name.
Turkey's vulnerability - by Mark Lowen, BBC News, Istanbul
The site of the attack reopened swiftly, with floral tributes laid on the ground and people bearing Turkish flags. The government is as always keen to give a sense that the situation is under control.
But beneath the surface, Turkey feels vulnerable and afraid that it can't stop the wave of bombings. The government has vowed revenge and President Recep Tayyip Erdogan says terrorism will be crushed.
But perhaps the most tumultuous year in Turkey's history means many will see the words as empty rhetoric. This is, though, a defiant nation. One protester told me terrorists "aimed to keep us at home, scared of going out. We can't do that. We must show unity against this threat".
After bombings by the PKK and IS and an attempted coup, Turkey finishes 2016 angry, grieving and even more politically polarised. A toxic mix for a country that has seemingly lost its way.
Mr Numan said that about 300-400kg (660-880lb) of explosives had been used in Saturday evening's attack.
It came two hours after the end of the match between top teams Bursaspor and Besiktas, when fans had already dispersed.
President Erdogan told reporters on Sunday that Turkey would fight "the scourge of terrorism to the end", and promised that the attackers would pay a "heavy price".
Thirty of those killed were police officers. Dozens of people remain in hospital, some in intensive care.
Turkey has declared a day of national mourning.
Interior Minister Suleyman Soylu said 13 people had been arrested after the latest blasts, but gave no details.
2016 Kurdish attacks in Turkey
17 February: TAK attack on vehicles carrying general staff personnel in Ankara kills 28 people
13 March: 37 people are killed by TAK militants in a suicide car bombing in Ankara
8 June: TAK bomb attack in Istanbul kills seven police officers and four civilians
30 July: Turkish army base attacked in south-east - unconfirmed reports say soldiers killed some 35 Kurdish fighters who tried to storm the base
9 October: Car bomb attack by PKK militants on checkpoint in south-east kills 10 soldiers and eight civilians