Meanwhile, UN-Arab League envoy Lakhdar Brahimi was in Iran as he presses efforts to build a consensus for a Geneva conference aimed at ending the conflict.
Fighters from both sides were killed in the border clashes, which came a day after Syria's regime and its opponents traded blame for a car bomb attack on a mosque that left dozens dead.
The Kurds "took control of the Al-Yaarubia border crossing with Iraq at dawn after clashes with the Islamic State in Iraq and the Levant, the Al-Nusra Front and other rebels," the Syrian Observatory for Human Rights said, citing activists.
Rebels battling to oust President Bashar al-Assad have increasingly turned their guns on each other in the past few months, with jihadists fighting the mainstream Free Syrian Army in the north, where the insurgents control vast swathes of territory.
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The seizure of the border post would be another blow for the Islamists. State television said late yesterday that Al-Nusra leader Abu Mohammed al-Jawlani had been killed, but the Al-Qaeda-linked group said he was in good health.
The conflict flared when Assad's opponents took up arms in response to his regime's brutal crackdown on Arab Spring-inspired protests that erupted in March 2011.
Today's violence comes a day after a car bomb outside a mosque in Suq Wadi Barada, a town near Damascus, killed at least 40 people and wounded dozens more, according to the Observatory.
State news agency SANA said "the car exploded while the terrorists were packing it with explosives," using the regime term for rebels.