His announcement, which came after a phone call with Turkish President Recep Tayyip Erdogan, was criticised even within his own camp and is already having major repercussions on the almost eight-year-old conflict.
He said such statements were "unacceptable".
He added that Pompeo is a senior intelligence officer with a mission to "cover up America's operational defeats via psychological operations", including by taking such measures against Iran.
Mr Bolton was on a visit to Ankara to seek guarantees over the Kurdish fighters, but President Erdogan declined to meet him.
Operation Olive Branch was conducted by Turkish Armed Forces-backed Syrian opposition group Free Syrian Army (FSA) starting on January 20, 2018 to remove the PKK's Syrian affiliate People's Protection Unit (YPG) elements from Afrin in northwestern Syria following the first operation conducted in northern Syria in 2016, the Operation Euphrates Shield that targeted Daesh terrorists in Syria's Al-Bab and Jarablus. The YPG denies any direct organisational links to the PKK. He suggested that the protection of Kurdish allies in the country would be a redline for the withdrawal.
Mr Pompeo really wants to turn the focus to countering Iran. He is also expected to travel to Saudi Arabia.
U.S. officials, speaking on condition of anonymity, confirmed that equipment was being moved out of Syria, a sign that despite mixed messages from Washington preparations for a withdrawal of troops was proceeding apace.
"Many details (are) still to be worked out but I'm optimistic that we can achieve a good outcome", he said.
In 2014, militants overran 100,000 sq km (39,000 sq miles) of Syria and neighbouring Iraq, and imposed their brutal rule on nearly 8 million people.
Media captionIs this the Islamic State group's last stand in Syria?
His visit follows an address in Cairo on Thursday in which he pledged continuing U.S. support for stabilising the region and countering the threat posed by Iran and its role in Syria, Lebanon, Iraq and Yemen.
Confirmation of the first withdrawals comes amid confusion over plans to implement President Donald Trump's pullout order and threats from Turkey to attack the Kurds, who have been America's partners on the ground in the war against ISIS in Syria.
Trump's national security advisor John Bolton on Sunday announced conditions for a withdrawal that appeared to delay it indefinitely.
He added, "If there are other terrorists who would attempt to intervene in our intervention, then it is our duty to eliminate them as well".
She charged that the US appeared to be "looking for a reason to stay" in Syria.
Journalist Jamal Khashoggi, a USA resident, entered the Saudi Consulate in Istanbul on October 2 seeking documents that would have allowed him to marry his Turkish fiancée, Hatice Cengiz.
The US did this after several attempts at training and arming Syrian Arab rebel groups to battle IS militants descended into chaos.
"They are taking their differing views of what the United States should do in Syria - a question that normally would be robustly hashed out inside the Situation Room - and instead entrepreneurially trying to present their own preferences as "Trump Policy" on the world stage".