Bolton said in Israel that the USA would pull out only after its troops had rooted out what's left of ISIL in Syria and after the administration had reached an agreement with Turkey to protect Kurdish militias who have fought alongside Americans against the extremists.
Mr Bolton's comments mark the first public confirmation that the drawdown has been slowed, as Trump faced widespread criticism from allies and the resignation of Defence Secretary Jim Mattis for a policy that was to have been conducted within weeks.
"One aim of Turkey's fight against the PKK and its Syrian extensions is to rescue the Kurds from the cruelty and oppression of this terrorist group", state-owned Anadolu news agency quoted Kalin as saying, in comments that emerged after Bolton made his remarks.
Bolton, often seen as a hawk in matters of United States defense, stated that the U.S. enjoys many forms of influence in Syria even after an army withdrawal and is committed to the safety and security of the Kurds even after a USA withdrawal.
The announcement came moments after the city's residents asked the Syrian government to retake Manbij following Trump's pledge to withdraw U.S. troops from the Arab country. "I never said we're doing it that quickly".
But while Bolton's comments may have come as a relief to some, a top House Democrat stressed that the priorities the national security adviser outlined were "obvious" - and simply highlighted how risky Trump's initial withdrawal announcement was.
"So the regime, the Assad regime, should be under no illusions on that question", said Bolton, who is on a four-day trip to Israel and Turkey.
Kalin said PYD and YPG were Syrian branches of PKK terrorist group, which continue their acts on the pretext of fighting against Daesh, added: "They can not represent Syrian Kurds".
"There is no doubt that a terror group can not be an ally of the US", Kalin said. Turkey sees the Kurdish forces in Syria as an extension of the separatist group the PKK.
Erdogan's spokesman Ibrahim Kalin said Turkey's targets are the YPG, the PKK and IS.
"There are objectives that we want to accomplish that condition the withdrawal", Bolton told reporters in Jerusalem.
The U.S.is also seeking a "satisfactory disposition" for roughly 800 ISIL prisoners held by the U.S. -backed Syrian opposition, Bolton said, adding talks were ongoing with European and regional partners about the issue.
Bolton was to have dinner with Israel's prime minister, Benjamin Netanyahu, on Sunday to discuss the pace of the US drawdown, American troop levels in the region, and the USA commitment to push back on Iranian regional expansionism. He watched a virtual reality tour of the historic site and dined there with his Israeli equivalent, as well as with US Ambassador to Israel David Friedman and Israel's Ambassador to the US, Ron Dermer. Israel captured the Old City from Jordan in the 1967 war.