Washington began carrying out air strikes against the extremist group in Iraq earlier this month, and the Syrian government has also stepped up raids against the jihadists on its own territory.
But there is little love lost, with Syria angered by US support for anti-government rebels.
For its part Washington accuses Damascus of having allowed Islamic State to flourish so as to paint its opponents as extremists.
IS posted a video yesterday showing the apparent execution of American journalist James Foley who has been missing since he was seized in Syria in November 2012.
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Damascus has looked with suspicion at the American air strikes that began in Iraq on August 8, concerned they could lead to broader US action against both jihadists and regime forces in Syria.
"In striking IS, Damascus is telling the Americans that it doesn't need its air force against the IS," said Waddah Abed Rabbo, director of Syria's pro-government Al-Watan newspaper.
"We have treated America as an adversary for three years and six months," said Bassam Abu Abdullah, director of the Centre for Strategic Studies in Damascus.
Earlier this year, European intelligence services began reaching out to Damascus, worried about the influx of Europeans coming to Syria to join the ranks of jihadist groups battling the regime.
But Syrian officials said they had no interest in cooperation on security issues without a political deal.
And the United States denies any interest in rapprochement with Damascus, even if they find themselves with a common enemy in the Islamic State.
She repeated the US government's line that the Syrian regime helped strengthen IS by failing to attack it until recently.
And she said US involvement in Iraq didn't mean US strikes in Syria.