AYN ISSA, Syria — Forces backed by the United States have nearly sealed off the northern Syrian city of Raqqa, trying to trap as many as 2,500 hard-core Islamic State militants defending the capital of their self-proclaimed caliphate.

The fighters, known as the Syrian Democratic Forces, are made up of Syrian Kurds and Arabs, and they have received crucial support from the American-led coalition fighting the Islamic State in Syria and Iraq. The coalition has already destroyed the two bridges that lead south from Raqqa, which is on the northern bank of the Euphrates River. The coalition also helped the forces establish control of two nearby dams.

“And we shoot every boat we find,” said Lt. Gen. Stephen J. Townsend, the American commander of the coalition force fighting the militants. “If you want to get out of Raqqa right now, you’ve got to build a poncho raft.”

As Iraqi forces are mopping up the last pockets of Islamic State resistance in the Iraqi city of Mosul, the battle for Raqqa gives the American-led coalition — and the Trump administration — an opportunity to deliver a blow to the Islamic State, also known as ISIS or ISIL, by capturing its most visible territorial claim to a caliphate.