But, he added, "we also know that those fighting alongside of us for all this time deserve to be protected as well".
Trump made the decision to withdraw some 2,000 American troops from Syria last month, amid consultations with the Turkish military over their planned operations in Syria.
Speaking in the United Arab Emirates, Mr Pompeo said he thought it would be possible to reach an agreement which would allow the Turks to defend themselves from terror threats while protecting Kurds - who have been fighting alongside USA troops - against the so-called Islamic State group.
Senior US officials were shocked too, among them Defense Secretary Jim Mattis, who quit in protest.
Pompeo said Friday that Washington recognized "the Turkish people's right and Erdogan's right to defend their country from terrorists".
He said the United States envoy for Syria, Jim Jeffrey, had travelled to northeast Syria this week and would soon go to Ankara for talks, including on moving forward a UN-led political process to end the eight-year long conflict in Syria. And while about 2,000 American troops are now based in the civil war-torn country, that number could increase before a final pull-out, according to the New York Times.
The announcement of a pullout is fueling concern about how quickly the US will abandon its Kurdish allies, amid contradictory statements recently by Trump administration officials on an exit timetable. "We are confident we can achieve an outcome that achieves both of those".
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"Out of concern for operational security, we will not discuss specific timelines, locations or troop movements", Ryan said.
"We have no problems with our Kurdish brothers, Arab brothers in Syria, Turkmens and other ethnic and religious groups".
Military spokesman Lt. Col. Jonathan Conricus said the latest tunnel originated from the Lebanese border town of Ramyeh, was 55 meters deep and ran 800 meters inside Lebanese territory and also "dozens" of meters into Israel.
President Recep Tayyip Erdoğan has called Bolton's remarks unacceptable, saying Turkey could not accept the U.S.' condition of protecting YPG terrorists, the Syrian affiliate of the PKK. "After all, the Kurds are an integral part of Syrian society", Zakharova said.
A Kurdish politician told Reuters last week the Kurds had presented Moscow with a roadmap for a deal with Damascus.
"President Macron spoke to him (Trump) several times and it seems that there has been a change that I think is positive", he said in a television interview on Thursday.