The Kurdish-led Syrian Democratic Forces (SDF) denied Monday any role in the deadly bomb attack in central Istanbul that killed six people and wounded 81, which Turkey has blamed on Kurdish militants.

"Our forces have nothing to do with the Istanbul bombing," said Mazloum Abdi, the chief commander of the US-allied SDF.

Turkey considers the Kurdish People's Protection Units (YPG) -- the main component of the SDF -- an extension of the Kurdistan Workers' Party (PKK).

Ankara has blamed the PKK for carrying out the attack Sunday in Istanbul. The PKK also denied involvement in the attack.

"It is out of question for us to target civilians in any way," it said.

There has been no claim of responsibility.

Turkish Interior Minister Suleyman Soylu claimed that "the order for the attack was given from Kobane," referring to a Kurdish-held city in Syria near the Turkish border.

As international condemnation of the attack poured in, Soylu, a fierce critic of Washington, likened US condolences for the victims to "the murderer arriving as one of the first at the scene of the crime."

The Turkish Minister said, as cited by the CNN Turk broadcaster, "We do not accept condolences from the US Embassy. We are not treacherous to anyone, but we no longer have any tolerance for these insidious acts."

The US has supported the YPG in the war in Syria, stoking friction between the NATO allies.

On its part, Kurdish authorities in Syria accused Turkey in a statement on Monday of "creating pretexts and excuses to prepare the ground for attacking us."

Turkish police, quoted by Turkey's NTV television channel, said the main suspect in the bombing on Istanbul's Istiklal Avenue was a Syrian woman, identified as Alham Albashir, sent by Kurdish militants.

According to police, Albashir said during questioning she was trained by Kurdish militants and entered Turkey through Afrin, another northern Syrian town.

The Kurdish administration claimed that Albashir does not appear in any of its registries.

Forty-seven people were detained in total, Turkish police said.

A Turkish official said the possibility of the Islamic State (IS) being responsible for the attack was "not entirely disregarded."