According to Reuters, US warplanes pounded Islamic State (IS) positions in Syria for a second day on Wednesday, but the strikes did not halt the fighters' advance in a Kurdish area where fleeing refugees told of villages being burned to the ground and captives beheaded.
US President Barack Obama, speaking at the United Nations, asked the world to join together to fight the militants and vowed to keep up military pressure against them.
"The only language understood by killers like this is the language of force, so the United States of America will work with a broad coalition to dismantle this network of death," Obama said in 40-minute speech to the UN General Assembly.
British Prime Minister David Cameron recalled Parliament to vote on Friday (September 26) on whether to join the coalition airstrikes.
"Our strategy must work in tandem with Arab states, always in support of local people, in line with our legal obligations and as part of a plan that involves our aid, our diplomacy and, yes, our military," Cameron said at the UN.
Syrian Kurds said IS had responded to US attacks by intensifying its assault near the Turkish border in northern Syria, where 140,000 civilians have fled in recent days in the fastest exodus of the three-year civil war.
Washington and its Arab allies killed scores of IS fighters in the opening 24 hours of air strikes, the first direct US foray into Syria two weeks after Obama pledged to hit the group on both sides of the Iraq-Syria border.
Yet, the intensifying advance on the northern town of Kobani showed the difficulty Washington faces in defeating IS in Syria, where it lacks strong military allies on the ground.
COMMENT: It is regretful that US President Barack Obama did not decisively order strikes inside Syria before 191,000 Syrian lost their lives.
Islamist militants in Algeria boasted in a video they had beheaded a French hostage, age 55, captured on Sunday to punish Paris for joining air strikes against IS in Iraq. French President François Hollande confirmed the execution.
The US said it was still assessing whether Mohsin al-Fadhli, a senior figure in the al-Qaeda-linked group Khorasan, had been killed in a US strike in Syria.
France, which has confined its air strikes to Iraq, said it would stay the course despite the killing of hostage Herve Gourdel, 55, a mountain guide captured on vacation in Algeria on Sunday by a group claiming loyalty to Islamic State.
In a video released by the Caliphate Soldiers group entitled "a message of blood to the French government", gunmen paraded Gourdel's severed head after making him kneel, pushing him on his side and holding him down.
US officials say they informed both Assad and his main ally Iran in advance of their intention to strike, but did not coordinate with them.
Jordan, Bahrain, the United Arab Emirates, Qatar and Saudi Arabia have joined in the coalition.