Earlier on Tuesday, a USA defense official told AFP that United States received assurance that all parties involved are going to stop shooting each other and focus on DAESH.
On Tuesday, US Central Command spokesman Colonel John Thomas said Turkish and Kurdish forces in the area had come to a "loose agreement" to stop fighting, according to Agence France-Presse.
INSIDE STORY: Does Turkey trust Washington? .
The White House also lauded the apparent halt in fighting between anti-ISIL forces in Syria.
Turkey, which is fighting a Kurdish insurgency at home, has openly said the operation dubbed "Euphrates Shield" has a dual goal of driving away Islamic State and preventing Kurdish forces extending their areas of control along the Turkish border. But Turkish military sources denied there was any such agreement, while a Turkish-backed Syrian rebel commander characterised it only as a "pause" and said that military operations would soon resume.
"We agreed on a ceasefire with the Turkish state via the United States and the worldwide coalition" that is fighting IS militants, council spokesman Ali Hajo said.
Commander al-Sakit also said that the PYD might use the previously delivered chemicals around the city of Manbij, adding: "However, the point here is that there is a risk that the PYD's likely use of those chemicals in and around Manbij could be attributed to Turkey and the possibility that propaganda will be made based on this issue must be taken into consideration".
Ankara has frequently voiced its concern over the YPG's activity along the Turkish border and insists that the YPG forces should not pass to the west of the Euphrates River.
The fighting comes when the United States and Russian Federation say they're working toward an end to Syria's more than five and half years of civil war.
Turkey's presidential spokesman has called on the U.S.to "revise" its policy of supporting Kurdish forces battling Turkish troops in Syria after Ankara's incursion last week into the war-torn state.
A senior Turkish military official also told the Sabah daily: "We are not aware of such an agreement".
The Turkish Foreign Ministry said in a statement Tuesday that comments from the US about the target of the Turkish military operation in Syria were "unacceptable".
The YPG has since been advancing into northern Syria territory controlled by the Kurdish Democratic Union Party (PYD).
"These contracts show how the United Nations operation has quietly secured deals with individuals and companies that have been designated off-limits by Europe and the USA", the Guardian said. "They are basically saying that as far as they are concerned there is no truce".
Col Ahmed added that he anticipates clearing the area west of the Euphrates of ISIL and YPG forces within the next three weeks. "Their strategy basically is to continue the fight until they push YPG across the Euphrates River".
In a separate statement late on Tuesday, the Turkish military said that three of its soldiers were wounded and a tank was slightly damaged in a rocket attack in western Jarablus, without mentioning which group was behind the strike.
The U.S. allies FSA and YPG have found themselves on opposite sides of an ongoing Turkish military operation near the border town of Jarablus in northern Syria's Aleppo province since the rebels captured the town from the Islamic State (ISIS/ISIL) last week during an offensive backed by the Obama administration.
US Defence Secretary Ash Carter called on Turkey on Monday to stay focused on fighting ISIL and not target the YPG.
Both sides are backed by the U.S. in their fight against ISIL, but Turkey, a key North Atlantic Treaty Organisation ally, views the YPG as a threat because of its close links to the Kurdistan Worker's Party (PKK), which has been fighting Turkish forces for the past three decades.
However, by giving rebels air and artillery strikes - and letting rebel units transit through Turkey to blindside ISIL forces in Jarablus - Ankara is allowing the rebels to make advances that would have been much more hard, if not impossible, without their help. State Department, the Pentagon, and the White House, Turkish clashes with US -backed Kurdish groups in northern Syria are hindering the fight against ISIS.
Syrian opposition activists have said at least 35 civilians were killed in northern Syria in the Turkish-led operation so far.
The Turkish military and its Syrian rebel allies are a week into a campaign created to drive IS militants and Kurdish YPG members, who are part of the US -backed Syrian Democratic Forces, out of the Syria-Turkey border town of Jarablus and its surrounding areas. "So long as they don't, they will be a target". "So, there is still a way forward to solve this crisis diplomatically".