“Governor McCrory’s actions today are a poor effort to save face after his sweeping attacks on the L.G.B.T. community, and they fall far short of correcting the damage done” by the law, Sarah Preston, the acting executive director of the American Civil Liberties Union of North Carolina, said in a statement on Tuesday.

But other opponents of the law said they were fleetingly encouraged by parts of Mr. McCrory’s announcement. Kyle Palazzolo, a staff lawyer at Lambda Legal, a gay rights group, said that the law’s “devastating blow” would not be resolved by Mr. McCrory’s order, but that it had brought “an improvement for the state employees it impacts.”

Since the measure became law, North Carolina has faced a barrage of criticism from business interests and warnings of boycotts and canceled investments. PayPal, an online-payment company, said it would abandon plans for a global operations center in the state, and the National Basketball Association suggested that it could move its 2017 All-Star Game from Charlotte. There, tourism officials said that organizers of at least four major events had cited the law when they dropped plans to be in the city.

On Tuesday, Deutsche Bank announced that it would “freeze plans to create 250 jobs” near Raleigh.

Mr. McCrory is not the first Republican governor to back away from a measure condemned as curbing gay rights. Last year, for example, Mike Pence of Indiana and Asa Hutchinson of Arkansas found themselves under similar pressures.

The North Carolina law that led to this year’s firestorm created a mandatory statewide anti-discrimination policy, but it did not include specific protections based on sexual orientation or gender identity. State lawmakers introduced their legislation after Charlotte, the state’s largest city, approved new legal protections for transgender people.