ISTANBUL — Turkey has confirmed that it struck positions in Syria held by Kurdish militias that over the last year have become the most important allies within Syria of the American-led coalition fighting the Islamic State.

The confirmation of the strikes, which the Kurds said took place over the weekend, adds a new level of complexity to the United States’ struggle to put together a coherent strategy to fight the Islamic State in Syria. It also increases tensions between the United States and Turkey, which are nominally allies in the battle against the militant group, but whose interests diverge substantially.

In an interview on a Turkish news channel Monday night, Prime Minister Ahmet Davutoglu of Turkey did not specify when the strikes had taken place, but he said they came after Turkey’s government in Ankara warned Kurdish fighters not to move west of the Euphrates River.

“We struck them twice,” Mr. Davutoglu said.

The Turkish strikes were in Tal Abyad, a largely Arab border town that the Kurds captured from the Islamic State over the summer. The strikes appear to have been limited — they were said to involve machine-gun fire from across the border and did not seem to cause much damage — but they could suggest a new determination by Turkey to expand military operations against the American-allied group.