"Timetables or the timing of the withdrawal occurs as a result of the fulfillment of the conditions and the establishment of the circumstances that we want to see", Bolton said.
The remarks represent a departure from the president's earlier statements about the timeline for USA involvement in Syria.
Bolton also said all 2,000 USA forces may not be pulled out, according to the report.
His comments mark the first public confirmation the withdrawal has been slowed, as President 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.
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.
Turkey's presidential spokesman called allegations that his country planned to attack the US-allied Kurds in Syria "irrational" and said Turkey was fighting terrorism for national security.
But Ankara insists that Turkey only targets Daesh and the YPG, which it sees as the offshoot of outlawed Kurdistan Workers' Party (PKK). He added that the meeting comes as Israel and the USA are "deepening' their "intelligence and operative cooperation".
Bolton said the US has asked the Kurds to "stand fast now" and refrain from seeking protection from Russian Federation or Syrian President Bashar al-Assad's government.
Criticizing the coalition operations in Raqqa and Mosul, Erdoğan said that they relied heavily on airstrikes and with "little or no regard for civilian casualties".
Turkish National Defense Minister Hulusi Akar also slammed Bolton's comments on Monday saying, "The fight of the Turkish Armed Forces (TSK) is not against our Kurdish brothers with whom we have shared the same geography and the same bread for centuries".
Among the policy decisions still to be made was what to do about the tens of thousands of Syrian Kurdish fighters that U.S. forces had trained, armed and advised to carry out the ground war against the Islamic State.
On Friday, Netanyahu held a phone talk with Russian President Vladimir Putin, for the first time since the us withdrawal announcement.
Dismantling ISIS has been an important achievement, and has come at a far lower cost compared to other USA military engagements in the region.
Many countries are reluctant to bring them back home while Syria's Kurds argue they do not have the capacity to keep them locked up much longer.
Bolton arrived in Israeli on a mission to calm Israeli concerns over U.S. President Donald Trump's decision to pull U.S.'s 2,000 troops out of Syria.
The president provided no firm timetable on Sunday for a pullback, simply telling reporters, "It's going quickly".