The US-led coalition said Turkey had nothing to fear from a border force in northern Syria.
He told reporters that the overall US mission remained defeating the Islamic State group and preventing its re-emergence.
Turkey has attacked the Afrin district in northern Syria, which is part of the Northern Syria Democratic Federation that is seeking to create a new revolutionary system of "democratic confederalism".
The United States must remain both diplomatically and militarily engaged in Syria to protect its own national security interests, Secretary of State Rex Tillerson said Wednesday.
It said the PYD/PKK has removed the pieces of rags symbolizing the terrorist organization. During his speech, he said: "Hey NATO! You are obliged to make a stance against those who harass and violate the borders of your members".
Another Kurdish official, who asked not to be identified because he was not authorized to comment on the matter, said the Kurds would not bow to Turkey or to the Syrian government.
Late on Tuesday, NATO responded to Turkey's concerns, saying it was a "highly valued ally" and the alliance was committed to Turkey's defence.
The British foreign ministry has said it will not be involved in the Syrian border force.
The radical Islamist women, as well as several men and children, are part of a group believed to number around 40 being held in northern Syria by Kurdish forces that liberated areas from ISIS control, backed by the USA -led coalition.
Turkey says the Kurdish People's Defense Units, or YPG, is a major threat to its security. Their sphere of influence expanded after they joined forces with the United States to fight Islamic State - although Washington opposes their autonomy plans. The United States however has relied on the YPG the backbone of a Syrian force that drove the Islamic State group from much of northern and eastern Syria with the help of USA -led airstrikes.
Qasemi urged all US forces to leave Syria immediately.
French prosecutor Francois Molins said past year that he expected hundreds of radicalized women to return to France as the group lost territory in Syria and Iraq.
Tillerson illustrated how the US would continue trying to isolate Assad's government even as the USA objective is "stabilization". He was referring to the planned 30,000-strong US-backed mostly Kurdish force.
On Tuesday, Foreign Minister Mevlut Cavusoglu suggested that a Turkish operation to root out Kurdish militants may extend from the Syrian border region of Afrin to east of the Euphrates, .
The YPG and Turkish forces inside Syria have accused each other of shelling around the Afrin region in recent days. But now the U.S. government has effectively told the Syrian Kurds that they can keep the huge chunk of Syria they control for the indefinite future.
The report also mentioned "a deeply flawed constitutional referendum that centralized power in the presidency, arbitrary prosecutions of rights activists... and continued purges of state employees, all of which have left citizens hesitant to express their views on sensitive topics".
"Along with our global partners, the United Kingdom supports the efforts of the UN-mediated Geneva process as we believe this is the best way of reaching a lasting political settlement to end the conflict".
Earlier in January, French authorities said there was no reason to bring those detained by Kurds back to France.