The Britain-based so-called Syrian Observatory for Human Rights said on Monday that the clashes are taking place in the volatile town of Boukamal.
The ISIL militants who control some parts of northeastern Syria took control of Boukamal last week.
This comes as Syrian fighter jets have conducted several airstrikes to pound militant hideouts in recent days at a border crossing between Iraq and Syria.
Iraqi Prime Minister Nouri al-Maliki has welcomed and supported the air raids on the ISIL and its associated groups along the border with Iraq.
The latest developments come as infighting has plagued militant groups fighting the Syrian government, as the army continues to gain more ground.
Clashes between the rival militant groups still continue despite an order by senior al-Qaeda leaders to stop the infighting.
More than 7,000 people have been killed since January in infighting among foreign-backed Takfiri militants who are wreaking havoc on Syria
The Syrian government says its troops are going ahead with their operations to flush the foreign-backed militants out of residential areas across the country.
Syria has been gripped by deadly violence since March 2011. Over 160,000 people have reportedly been killed and millions displaced due to the violence fueled by the Western-backed militants.
President Bashar al-Assad has recently said the Takfiri war in his country has strongly shifted in favor of government forces as they have made continuous gains in their fight against the terrorists.