KAMPALA, Uganda — Fighting inched perilously close to one of Congo’s largest cities on Sunday, and United Nations forces turned to heavy aerial bombardments to stop a rebel advance that broke into a sprint over the weekend, according to witnesses and officials of Congo’s army.

The rebels, members of the March 23 Movement, or M23, have advanced 18 miles along eastern Congo’s principal road since Saturday, capturing villages and beating back a seemingly broken Congolese Army. They are now only a few miles from Goma, the capital of North Kivu Province, which is home to nearly one million people and United Nations peacekeepers who have a mandate to use force to protect civilians.

It is the heaviest fighting in eastern Congo since Goma faced a similar rebel offensive in 2008.

“We are losing,” said Col. Olivier Hamuli, a spokesman for the Congolese Army.

The fighting had waned by early Sunday evening, and a spokesman for the rebels said they would not attack the city or the airport.