The attack on the soldiers would be the first known casualties sustained by the anti-ISIS coalition since President Trump announced his decision last month to pull 2,000 US troops out of Syria and declaring the terror group was defeated.
Trump's announcement on December 19 that the United States would immediately withdraw its troops from Syria led to concerns among allies, and he has since spoken of "slowly" sending troops home "over a period of time".
"There are objectives that we want to accomplish that condition the withdrawal", Bolton told reporters in Jerusalem.
The United States of America leaves some of the forces in southern Syria for an unknown period of time after withdrawal of the main troops, reports NBC with the reference to its sources in the Pentagon.
President Donald Trump's abrupt decision to announce a US pullout from Syria left many questions open, chiefly whether Kurdish fighters who had been operating in northern Syria alongside USA forces would now be attacked by their long-time enemy, Turkey.
U.S. Defense Secretary Jim Mattis resigned shortly afterward.
Ankara views the YPG as the Syrian branch of the PKK, which regularly clashes with Turkish forces in the Kurdish-dominated southeast of Turkey.
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.
Bolton, on a trip to Israel and Turkey, said he would stress in talks with Turkish officials, including President Tayyip Erdogan, that Kurdish forces must be protected.
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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. The U.S. military has already received orders on the drawdown.
Kurdish news outlet Rudaw reported that the British soldiers were hurt in an attack on a Syrian Democratic Forces (SDF) base in the town of Deir al-Zour, which also left a Kurdish fighter dead.
"To argue that a terrorist organization represents Kurds is, above all, disrespectful to our Kurdish brothers", Kalın said.
Bolton added that Trump is fully committed to the fight against terror, and as such "wants the ISIS caliphate destroyed".
Bolton said the USA wants its Kurdish allies in Syria protected from any planned Turkish offensive - a warning to be delivered to Turkey's president, Recep Tayyip Erdogan.
In this March 31, 2018 photo, a Syrian woman with her kids walks in front of buildings that were destroyed during a battle between the US -backed Syrian Democratic Forces fighters and ISIL militants in Manbij, north Syria.
He said the withdrawal would take place in northeastern Syria, while some forces could remain to the south at the al-Tanf garrison as part of efforts to counter Iran's presence.
The Palestinian Foreign Ministry on Sunday decried Israeli calls for demolishing sections of walls of Jerusalem's Old City. Mr. Trump himself, however, also toured the area in a previous visit.
Israel annexed east Jerusalem after capturing it from Jordan in the 1967 war, a move not recognized by most of the global community.