The Kurdistan Freedom Falcons, or TAK, said two of its members had sacrificed their lives in the Saturday night attack that targeted security forces outside the Besiktas stadium shortly after the conclusion of a match.
"I heard two explosions in less than one minute, followed by the sound of gunshots", one witness told AFP on condition of anonymity.
"They won't be able to divide Turkey, they won't be able to break it into pieces", one man told AFP, who gave his name only as Muammed. Suleyman Soylu says the source appears to have been a auto bomb that targeted a riot police bus outside Vodafone Stadium.
Thirty of those killed in the attack were police officers, officials say.
It read: "After yesterday's inhumane attacks, #Besiktas Vodafone Arena is decorated w/ Turkish flags today. The most important topic is on how we will stand against terrorist attacks, and I want the people to know that we will fight this until it ends", Erdogan said.
Turkey's ruling AK Party, the main secular opposition and the nationalist opposition said on Sunday they were in "full support" of security forces and their battle against terrorism, in a joint statement to parliament. A riot police bus appears to have been the target. Authorities, he said, had determined that about 300-400 kilograms of explosives were used in the attack. It is also about a kilometre (half a mile) from the busy Taksim Square, a magnet for tourists.
Israel's Prime Minister Benjamin Netanyahu also condemned the bombings but said he expected Turkey to reciprocate when the Jewish state also came under attack.
"We have once again witnessed tonight in Istanbul the ugly face of terror, which tramples on every value and decency", he said. The second blast was thought to be a vehicle bomb.
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The statement came after the Kremlin demanded an "explanation" from Erdogan over his comments on Tuesday. We hope that our Turkish partners will furnish us with an explanation regarding this".
Interior minister Suleyman Soylu said at a press conference reported by several news outlets in Turkey: "The attack on our country's children yesterday evening resulted in the martyrdom of 38 people".
Police forensic officers at work following explosions near the Vodafone Arena, the home of the Besiktas football club in Istanbul. Turkish officials frequently accuse the West of directly and indirectly supporting the Kurdish insurgency and of interfering in Ankara's fight against terrorism. The party, which had both of its leaders detained in terror probes and multiple elected officials arrested or removed from office in the southeast, denies the charge.
The crackdown against Kurdish politicians has coincided with widespread purges of state institutions following a failed coup in July that the government blames on followers of a US-based Muslim cleric.
Turkish police officers cordon off the roads around the stadium.
Bursaspor said on Saturday night that none of their supporters had been injured in the attack.
The outlawed party has waged a decades-long insurgency.
NATO Secretary General Jens Stoltenberg also condemned Saturday's "horrific acts of terror" in Istanbul. One of the blasts was thought to be a suicide bomber. The United States condemned the attack and said it stood with its North Atlantic Treaty Organisation ally.
He conveyed his sorrow and sympathy to the families of the victims, wishing a speedy recovery for the injured. Rescue services and ambulances rush to the scene of explosions near the Besiktas football club stadium after attacks in Istanbul, late Saturday, Dec. 10, 2016.