The US informs Turkey monthly of the weapons it sends to the terrorist organization with a list including photographic evidence and serial numbers.
The first inventory report was sent this month, said Mattis, and added that the aim was to capture Raqqah by the end of May.
Mattis said US advisors were active in the region to ensure that the weapons distributed remain within Syria.
The US will remain transparent within Turkey, and 80 percent of the forces that will seize Raqqah are composed of Arabs, said Mattis.
A US-backed alliance with the YPG dominated Syrian Democratic Forces (SDF) is a tactical relationship, assured Mattis.
The US Secretary of Defense expressed that he would like to meet with his Turkish counterpart Işık next week in Brussels. In previous meetings, Mattis assured Işık that the US will inform Turkey of all weapons sent to the terrorist organization.
Mattis emphasized that the relationship between the US and Turkey is a strategic partnership that will outlast the defeat of Daesh.
He disclosed that the US has taken intensive and decisive measures against the concerns expressed by Işık about the security of Turkey and said that the lists of military equipment given to the YPG will be shared with Turkey each month.
The YPG is a part of the US-backed Syrian Democratic Forces (SDF) which launched an operation earlier this month to capture Raqqah.
Turkey has said that it would retaliate against the YPG if it felt a threat from the group.