Mattis, in a letter addressed to his Turkish counterpart Fikri Isik on Thursday, stated that the United States has taken intensive and determined measures regarding Turkey's security concerns, and would provide the Ankara government with a monthly list of the weapons and equipment supplied to the YPG.
The US defense chief further noted that the first inventory list was submitted to Turkish officials earlier this month.
Mattis also said that Arab fighters would form 80 percent of the so-called Syrian Democratic Forces (SDF), which the YPG is a major component of, stressing that Raqqah would be held by Arab forces once the city is liberated from ISIS' clutches.
It is estimated that a population of 300,000 civilians are trapped inside Raqqah, including 80,000 displaced from other parts of Syria. Thousands have fled in recent months, and the United Nations Office for the Coordination of Humanitarian Affairs believes about 160,000 people remain in the city.
On June 6, the SDF said it had launched an operation aimed at pushing ISIS out of Raqqah.
The city of Raqqah, which lies on the northern bank of the Euphrates River, was overrun by ISIS terrorists in March 2013, and was proclaimed the center for most of the Takfiris’ administrative and control tasks the following year.
Turkish officials have frequently voiced strong opposition to the involvement of the Kurdish People's Protection Units in the US-led offensive to retake Raqqah.
Ankara views the YPG as the Syrian branch of the Kurdistan Workers' Party (PKK) militant group, which has been fighting for an autonomous region inside Turkey since 1984.
Speaking to reporters while on a visit to Montenegro on May 10, Turkish Foreign Minister Mevlut Cavusoglu stated that Washington knows Ankara’s position on the YPG very well so it should not take wrong steps in Syria.
The top Turkish diplomat added that the United States needed to distinguish between the YPG and their Arab allies in the SDF, and that the Arabs should be the ones to enter Raqqah.
Turkish President Recep Tayyip Erdogan also set out Turkey's objections at a White House meeting with his counterpart Donald Trump last month.