AT&T will offer a $5 credit to customers affected by a widespread outage on Thursday that was caused by technical issues the company encountered while trying to expand its network, its chief executive said on Sunday.

The outage, which started around 3:30 a.m. Eastern time, temporarily cut off connections for users across the United States.

Some of the affected cities included Atlanta, Los Angeles and New York, according to Downdetector.com, which tracks user reports of telecommunication and internet disruptions.

At its peak, the site had received about 70,000 reports of disrupted service for AT&T. Service was fully restored after about seven hours.

“No matter the timing, one thing is clear — we let down many of our customers, including many of you and your families,” the chief executive of AT&T, John T. Stankey, wrote in a letter dated Sunday. “For that, we apologize.”

In an effort to “make it right” AT&T is offering customers a $5 credit on their AT&T Wireless account, according to the company’s website.

“For the portion of consumer and small business customers most impacted by the outage, we are automatically applying an account credit to compensate them for the inconvenience they experienced,” the company said.

It will take one to two billing cycles for the credit to appear, depending on when a customer’s bill closes, the company said.

Prepaid customers will have options available if they were affected, Mr. Stankey wrote, but did not specifically identify those options.

AT&T also said it was “working closely” with Mid-Market and Enterprise customers, which are internet plans for businesses, to address their concerns.

It was not immediately clear how much the credits would amount to in lost revenue. A company representative could not be reached on Sunday.

In a statement, AT&T emphasized that the outage wasn’t caused by a cyberattack.

“Our initial review of the cause of Thursday’s outage indicates it was due to the application and execution of an incorrect process used while working to expand our network,” Mr. Stankey wrote in his letter.

The credit is meant to refund customers for the day that the service was lost, he wrote.

“I believe that crediting those customers for essentially a full day of service is the right thing to do,” Mr. Stankey wrote.