Brett McGurk, the US' special presidential envoy for the global coalition to counter Isis also confirmed the news on Twitter.
Last month, Erdogan said if Turkey and the U.S. joined forces, they could turn Raqa into a "graveyard" for jihadists. The Turkish military has repeatedly claimed that sophisticated anti-tank missiles delivered by its Western allies to Syrian Kurdish forces have fallen into the hands of the PKK fighting in Turkey.
Fikri Isik also told private NTV television on Wednesday that Turkey has the power to defend its national interests in Syria, though he did not elaborate.
However, the Syrian Kurdish group labelled a terror organisation by Turkey hailed the United States decision to arm it with heavy weapons to fight IS.
But on April 27, Turkish warplanes struck YPG forces in Syria and also hit Kurdish forces in neighbouring Iraq in what Ankara described as "terrorist havens". "If there is a decision otherwise, this will surely have consequences and will yield a negative result for the U.S. as well", Prime Minister Binali Yildirim said.
Tabqa, a strategic town for ISIS in Syria, has been retaken by US -backed Syrian Kurdish forces, giving allies a new route to the militant stronghold of Raqqa.
Dorrian said he did not have an exact timeline detailing when the Kurdish fighters would receive the weapons, but said any equipment provided by the United States would be "metered out" and aligned with specific tasks involved in the operation to retake Raqqa, the de facto capital of ISIS's self-proclaimed caliphate.
Dorrian said Wednesday that directly arming the YPG would "accelerate" the assault on Raqqa.
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Deputy Prime Minister Nurettin Canikli said the United States should review its move.
The YPG says the USA commitment to the group, and its umbrella coalition the Syrian Democratic Forces, will allow it to expand its operations against IS.
"Both the PKK and YPG are terrorist organisations and they are no different apart from their names", he said.
The SDF operation began on March 22 with a surprise aerial infiltration behind enemy lines to the south of Lake Assad, severs ISIS's ability to reinforce Raqqa and denies ISIS a key coordination hub that its foreign terrorist fighters used since 2013 to plan local operations and external attacks against the West. "Every weapon seized by them is a threat to Turkey". Turkish ministers from time to time have threatened Washington over its use, but analysts predict Ankara remains reluctant to take such a drastic step and risk wrecking relations with Trump.
Despite fierce objections from North Atlantic Treaty Organisation ally Turkey, the United States this week approved supplying arms to the powerful Kurdish YPG militia, a key component of the SDF and their campaign.
With air strikes and special forces from the USA -led coalition, the SDF are advancing on Raqqa to ultimately take the city, which is also the Islamic State's base of operations in Syria.
But this sparked ire from Turkey, which regards the YPG as the Syrian branch of the Kurdistan Workers Party (PKK), which since 1984 has waged an insurgency inside Turkey, leaving tens of thousands dead.
Mass killings in the Syrian conflict by government forces and militants affiliated with ISIS and other groups have been long reported. "We want to believe that our allies would prefer be side by side with ourselves rather than with the terror groups", he added.