The Syrian Observatory for Human Rights said half the city of Afrin was captured but that there were still some "violent clashes."
Violence in Syria isn't just a factor of the country's civil war. Several conflicts are raging.
Turkish officials also told the U.S. to withdraw its forces from Manbij, a border area in Syria.
Turkey considers the U.S.-backed Kurdish fighters to be terrorists.
Tillerson gave the policy speech at Stanford University.
President Donald Trump reportedly told Turkish President Recep Tayyip Erdoğan about that change over a phone call.
Since the referendum, Iraqi forces have taken over strategic locations that were under Kurdish control.
Iraqi soldiers rolled into Kirkuk to take back control of the area's oil fields, air base, power plant and refinery.
More than 92 percent of voters approved Monday's referendum, and Kurdish leaders hope that will kick-start independence talks.
The referendum, if successful, could kick-start secession talks between Baghdad and the Kurdish regional capital, Irbil.
The U.S. asked the government of Iraq's Kurdistan region to hold off on its push for independence to instead focus on fighting ISIS.
The YPG is a dominant force within the Syrian Democratic Forces.