The issue risks further stoking tensions between Ankara and Washington less than a week before President Recep Tayyip Erdogan heads to Washington to meet his US counterpart Donald Trump, in their first face-to-face encounter as heads of state.
The Kurdish Peoples' Protection Units (YPG) is seen by Washington as the best ally against Islamic State group jihadists in Syria and the prime attacking force in any upcoming assault on their stronghold of Raqa.
The dispute poisoned ties between the two NATO allies under the administration of former president Barack Obama but Ankara had hoped for smoother ties under Trump.
Prime Minister Binali Yildirim said it was "out of the question" for Turkey to accept any direct or indirect help for the PKK.
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"The United States and Turkey are two major partners in NATO. We don't believe America would choose a terror group over our strategic relations," he told reporters.
"We expect that this mistake is to be rectified," he said.
Turkish Foreign Minister Mevlut Cavusoglu added that "every weapon that turns up in their hands is a threat directed toward Turkey".
Pentagon chief Jim Mattis sought to allay Turkish concerns, saying at a news conference in Lithuania the US would work very closely with Turkey over security on its border with Syria.
"We have very open discussions about options and we will work together, we will work out any of the concerns," he said.
The YPG hailed the move as "historic" and said it would now play "a more influential, powerful, and decisive role" in fighting IS.
YPG spokesman Redur Xelil described the move as "somewhat late", but would still "provide a strong impetus" to all forces fighting IS.
The SDF, a US-backed group dominated by YPG but which also contains Arab elements, said that receiving US arms and military equipment would "hasten the defeat" of the jihadists.
While the government expressed predictable anger, the deputy head of the opposition Republican People's Party (CHP) Ozturk Yilmaz said it should go even further by postponing Erdogan's visit to the US.
A high-level Turkish delegation including Chief of Staff General Hulusi Akar, presidential spokesman Ibrahim Kalin and Turkey's spy chief Hakan Fidan had been in the US laying the groundwork for the meeting.