"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 outlawed Kurdistan Workers' Party (PKK).

Ankara has blamed the PKK, which has waged an insurgency in Turkey for decades, for carrying out the attack Sunday in Istanbul. The PKK also denied involvement in the attack.

There has been no claim of responsibility.

The SDF is the de facto army of the semi-autonomous Kurdish administration in northeastern Syria.

It provided crucial assistance to a US-led coalition against jihadists of the Islamic State (IS) group.

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

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

Turkey has launched waves of attacks on Syria since 2016 targeting Kurdish militias as well as IS jihadists, and Ankara and forces backed by it have seized territory along the Syrian border.

Since May, Turkish President Recep Tayyip Erdogan has threatened to launch a new operation into northern Syria.

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 sent by Kurdish militants.

The Kurdish administration said the suspect, identified by Ankara as Alham Albashir, does not appear in any of its registries.

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