Xelil said the new battalions were not taking part in the operation to encircle Raqqa. He declined to say if the new training program was supported by any foreign militaries.
The YPG's 60,000-strong strength includes the YPJ - the all-female militia that numbers around 24,000, Xelil said. Both male and female fighters are being sought in the recruitment drive.
The dominant Syrian Kurdish groups and their allies aim to deepen their autonomy through the establishment of a new system of federal government in the north. The Kurds, systematically persecuted for years by the Syrian state, say their aim is not independence.
Hemo told Reuters that the YPG aimed to "fight terrorism" everywhere in Syria, while its political priority was "guaranteeing the rights of the Kurdish people in Syria legally, constitutionally".
He also signaled a readiness on the part of the YPG to reach a long-term accommodation with the Syrian government, saying "there will be no problem with the regime" once Kurdish rights are secured.
Syrian President Bashar al-Assad has stated his opposition to the regional federal model which the dominant Syrian Kurdish groups say should be the solution to the Syrian war. Assad has vowed to take back all of Syria