Opposition forces need "efficient weapons to face these attacks including air raids, so we can change the balance of power on the ground," Jarba told a US think-tank at the start of his first official visit to Washington.
"This would allow for a political solution," he insisted.
Jarba, head of the Syrian National Coalition (SNC), is to hold high-level talks this week with Secretary of State John Kerry and national security chief Susan Rice.
Jarba urged the international community to unite to stop Syrian President Bashar al-Assad as he runs for office "on the dead bodies of Syrian," condemning next month's elections as a "farce" that would give Assad "license to kill for many years to come."
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He stressed that Syrians were not calling on the United States or the West "to send their sons to Syria."
"We do not want Americans to die in Syria," he insisted.
But, he said, "we do have a problem with the air forces, the air raids and the barrel bombs. This is making our lives a nightmare, so we want weapons that would neutralise" the air forces.
US officials have refused to be drawn on the type of non-lethal aid or weapons being supplied by Washington, apart from detailing such things as night-vision goggles and communications equipment.
A senior US administration official this week acknowledged there was "an asymmetry militarily" between the opposition rebels and the Assad regime, and insisted Washington was looking at ways to change the balance of power on the ground.