Bolton maintained there is no fixed timetable for completing the drawdown, but insisted it was not an indefinite commitment to the region.
Trump wants to pull 2,000 US troops out of Syria, where Iran and Hezbollah have propped up Assad during Syria's seven-year civil war, which is winding down.
Fighting alongside Arab and Kurdish forces, American troops have been largely successful in pushing back the Islamic State and stabilizing the country, since entering Syria in 2014.
Despite the announcement, the war against ISIS in Syria has continued, with US-backed forces recapturing ISIS-held towns and the US-led coalition conducting 469 air and artillery strikes on ISIS targets between December 16 and December 29, the coalition said.
Trump also clarified Sunday that "we won't be finally pulled out until [the Islamic State] is gone". Turkey considers the Syrian Kurdish People's Protection Units, or YPG, a terrorist group linked to an insurgency within its own borders.
Turkey has been hoping for a quick withdrawal of US troops from Syria because an offensive against the YPG could help Erdogan consolidate nationalist voters' support for his ruling AK Party in local elections in March.
According to the official, the guarantees include giving assurance to avoid military action in Syria unless fully coordinated with Washington. He is to deliver a warning to Turkish President Recep Tayyip Erdogan this week.
If the U.S. plans on making a withdrawal conditional on Turkish guarantees of safety for the YPG in Syria, one of two things will happen. "I think they know who their friends are", Bolton said, referring to the Kurds. "Acknowledging Israeli sovereignty over the strategically-critical heights would obviously be in Israel's interest, but also in the interest of the United States", explained Jonathan Ruhe, Associate Director, JINSA's Gemunder Center for Defense and Strategy.
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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. Lindsey Graham (R-S.C.), who is normally a close ally of the president, have said a quick withdrawal would be a mistake, in part because it could leave the region vulnerable to a possible ISIS resurgence.
Bolton, Joint Chiefs of Staff Chairman Joseph Dunford and James Jeffrey, the US special representative for Syria engagement, are scheduled to meet Turkish officials in Ankara on Tuesday.
Ziya Meral, senior resident fellow at the British Army's Centre for Historical Analysis and Conflict Research, said the priorities of the U.S. and Turkey over northern Syria are hard to reconcile, not least because it is not clear what it is that the Trump administration actually want to see in the long term.
Bolton said there was no timetable for the United States withdrawal from Syria but that there was not an unlimited commitment. He defended the legal basis for the deployment, saying it's justified by the president's constitutional authority.
Bolton symbolically showed support for Israeli claims over Jerusalem on Sunday, by visiting the Western Wall and touring the adjacent underground tunnels, before having lunch with other Israeli and United States officials.
A senior Kurdish official said Monday that Syria's Kurds are awaiting clarifications from the U.S. Speaking to The Associated Press from northern Syria Monday, Badran Ciya Kurd said the Kurds have not been informed of any change in the U.S. position and were in the dark about Bolton's latest comments.
Bolton also suggested some troops would remain in Syria indefinitely.
Bolton on Sunday also toured the ancient tunnels beneath the Western Wall in Jerusalem's Old City.