AT&T’s U-verse service for phone, Internet and TV, has been knocked out for days in several cities. But the company says the service should be working again very soon for all customers.

AT&T on Wednesday said that U-verse had gone down in some states in the Southeast and Southwest, citing a faulty software update. Mark Siegel, an AT&T spokesman, said on Thursday that U-verse should be working for most customers by now, and for the rest, it should be restored in the next few hours. People affected by the service failure will get credit on their accounts, the company said.

“U-verse service has been restored for the vast majority of our customers affected by the outage,” Mr. Siegel said in a statement. “We expect any remaining customer issues will be resolved this morning. We will provide a credit to customers who were affected. We know our customers count on their U-verse service and we apologize for the inconvenience.”

Indeed, Twitter lighted up Thursday morning with some U-verse customers reporting that they were back online.