Sunday's announcement brings to 31 the number of Turkish soldiers killed since the operation against the Syrian Kurdish militia started on January 20 with Ankara's cross-border incursion into the enclave of Afrin.
"We don't have exact evidence or documents to determine that it went down with any outside interference", Binali Yildirim told reporters in the western province of Mugla.
Eleven Turkish soldiers were killed on Saturday, including two military personnel when a helicopter was downed, in the bloodiest day in Ankara's offensive against a Kurdish militia in northern Syria.
However, in a posting on Twitter, Mustefa Bali, spokesman for the US-backed Syrian Democratic Forces dominated by the YPG, said a helicopter had been hit in the Rajo area of northwest Afrin, near the Turkish border.
"Of course, these kinds of things will happen. We will have losses, but we will cause the other side to have losses as well", he said in a televised speech, vowing to make the perpetrators pay "a much heavier price".
Since the beginning of the operation, the Turkish Armed Forces and Free Syrian Army have managed to capture 48 different strategic areas from terrorists including a town center, 31 villages, three rural areas and 13 hills.
While the USA has worked to strengthen the Syrian Kurdish force, called the YPG, to help combat the Islamic State in Syria and Iraq (ISIS), Turkey considers the YPG to be a terrorist organization within its borders.
A member of Afrin's civil administration, Hevi Mustafa, was quoted by Reuters as saying the Turkish offensive had so far killed 160 people, including 26 children and 17 women.
The operation is being carried out under the framework of Turkey's rights based on global law, UN Security Council resolutions, its self-defense rights under the UN charter, and respect for Syria's territorial integrity, it said.