BEIRUT, Lebanon — As fighting raged in the suburbs of the Syrian capital, Damascus, and gunfire could be heard from the city center, rebels seeking the overthrow of President Bashar al-Assad were reported Friday to have declared the main airport a “fair target,” warning travelers that they used it at their peril.

Against the backdrop of battlefield uncertainty, diplomacy also seemed to have made little perceptible progress. Secretary of State Hillary Rodham Clinton repeated calls for the ouster of Mr. Assad, but said there had been no “great breakthrough” in talks she held Thursday in Dublin with her Russian counterpart, Sergey V. Lavrov, and Lakhdar Brahimi, the special Syria envoy of the United Nations and the Arab League.

“It was an important meeting, but just the beginning,” she said, speaking in Belfast, Northern Ireland, before flying back to Washington.

“I don’t think anyone believes that there was some great breakthrough,” she said. “Nobody should have any illusions about how hard this remains. But all of us with any influence on the process, with any influence on the regime or the opposition, needs to be engaged with Brahimi for a concerted, sincere push to see what is possible.