Fighting on Multiple Fronts in Syria

BEIRUT, Lebanon — Fighting continued Saturday across Syria, with the militant group Islamic State assaulting a Kurdish enclave on the Turkish border, American-led airstrikes hitting Islamic State positions in northeastern Syria and Syrian government airstrikes pounding other insurgents near Damascus, Syria’s capital.

Video surfaced of Peter Kassig, an American medical worker held by the Islamic State, in which the militants threatened that he would be the next hostage to be killed. The beheadings of two American journalists helped to set off the expansion of American-led strikes on the Islamic State, also known as ISIS, from targets in Iraq to the militants’ positions in Syria.

In Damascus, President Bashar al-Assad of Syria made a rare public appearance, joining prayers for the Eid al-Adha holiday at the Numan Bin Bashir mosque in scenes broadcast on Syrian state television. His last public appearance was in July at the end of the Ramadan holiday.

Turkish officials were weighing a ground intervention in Syria as Islamic State militants shelled a Kurdish enclave on the border. The Syrian government had warned on Friday that any military intervention on its soil by Turkey would be considered an act of “aggression.”

The warning came after Prime Minister Ahmet Davutoglu said that Turkey would do whatever possible to prevent the Kurdish enclave of Kobani from falling to the Islamic State militants. Kurds, though, are suspicious of Turkish intentions. They have said that Turkey is the main route for the passage of Islamic State militants into Syria and that Turkey prefers the militants to the semiautonomous Kurdish area that has evolved in the area during three years of chaos in Syria.

Near Aleppo, Syria’s largest city, insurgents who are not part of the Islamic State group were struggling to fight off a government offensive. The Syrian Army on Friday moved into a village north of Aleppo long held by the insurgents.

The other insurgents, some of whom President Obama says he is counting on as a ground force against the Islamic State militants in Syria, contend that by striking the Islamic State but not Mr. Assad, the United States is aiding the Syrian president in his effort to crush the revolt against him.

The war in Syria began with political protests against Mr. Assad’s rule but transformed into a civil war after government crackdowns on demonstrators, as Mr. Assad’s opponents took up arms and the army responded with heavy weapons. Jihadist groups arose, eventually paving the way for the foreign-led Islamic State, which has seized large portions of Iraq and Syria.

The Syrian government has focused on fighting insurgents who are not part of the Islamic State group, part of what its opponents and some of its supporters call a strategy to leave the West with a choice between itself and the extremist Islamic State. But lately, Islamic State fighters have routed government bases, increasing fears among Mr. Assad’s base, and the government has increased airstrikes against the militants.

While the Syrian government says American attacks on its soil without coordination are a violation of its sovereignty, some officials have recently said that as long as the coalition led by the United States is hitting the Islamic State, it is effectively helping the Syrian government.