A joint Kurdish-Arab militia has begun a new phase in the operation to dislodge the Islamic State from its stronghold in Raqqa, Syria, moving to encircle the city and largely cut off the resupply of arms, supplies and fighters, American military officials confirmed on Sunday.

Defense Secretary Ashton B. Carter said on Sunday that he welcomed the start of the militia’s operation. “The effort to isolate, and ultimately liberate, Raqqa marks the next step in our coalition campaign plan,” Mr. Carter said in a statement.

American warplanes are flying bombing missions against the Islamic State’s “leadership, command and control, and resources” in Raqqa and outside the city in support of the militia, the Syrian Democratic Forces, said Col. John Dorrian, a military spokesman in Baghdad.

Colonel Dorrian said in an email that it might be some time before the 30,000- to 40,000-member force reached Raqqa, and that the American-led coalition would continue to train and recruit more forces — especially Arab troops — for an eventual attack on the city.