Syrian opposition leaders Tuesday openly took issue with the US government's failure to launch a missile attack on the Syrian regime and pressed for assurances of US support in talks with US Secretary of State John Kerry.

Syrian opposition chief Ahmad Jarba led a four-strong delegation to meet Kerry on the sidelines of the UN General Assembly where the civil war in Syria is one of the top issues on the agenda.

Rebel forces are now fighting on two fronts, a senior State Department official said, highlighting that as well as battling the Syrian regime, rebel military chief General Selim Idriss and his forces were locked in combat against Islamist groups.

"Right now there's a real firefight going on up along the border Turkey and Syria between Al-Qaeda extremists and forces loyal to Selim Idriss," he said.

"That is battle that is ongoing right now, and it's very confusing," he said, adding the rebels were bringing in reinforcements but it was "a hard slog."

"It's the hardest fighting we've ever seen between Selim Idriss's elements of the Free Syrian Army and the Islamic State of Iraq in the Levant," he added.

"The extremists are doing the government's work now."

President Barack Obama on Tuesday unveiled a further $340 million in humanitarian aid for the refugees caught up in the war, in which 110,000 people have now been killed.

But the opposition has long pressed for more military back-up from the United States.

"They certainly did express disappointment that there hadn't been a military strike," the official said, after Obama last month backed away from taking military action to neutralize Assad's chemical weapons stockpile.

The opposition also "wanted a reaffirmation of our stance concerning Bashar al-Assad's legitimacy or lack thereof. Which Secretary Kerry gave them both barrels blazing."

Kerry assured the opposition leaders that after Assad "has used chemical weapons on his own people, after he has killed tens of thousands, it is impossible for us to imagine that he would play any role in a subsequent transition government," the official said.

The talks also focused on preparations for a peace conference dubbed Geneva II, as a date for such talks bringing together the opposition and the regime has repeatedly slipped.

Russia and the United States, which initiated the idea of the peace talks, are focused currently on getting a UN resolution to back a deal on bringing Syria's chemical weapons under control.

"Geneva II, or the Geneva peace conference, that will come next," the US official said.

He defended the US position to first focus on the chemical weapons deal, saying that it is "not illogical for both the Russians and the US to say 'wait before we can get to the peace conference we have to make sure we do not have more of these large scale gas attacks.'"