United Airlines has flown into another public-relations storm — it’s facing a lawsuit after a gay dad was accused by a flight attendant of having his hand too close to his 5-year-old son’s genitals on a flight from Newark to his home in North Carolina.

Henry Amador-Batten told The Post Saturday an airline representative called him to offer what she called an “apology.”

“It was not an apology,’’ the angry dad told The Post.

“She just wanted to make the problem go away. She asked me if I would keep it ‘low key’ ” to help her keep her job, he said.

“I don’t know how anyone could consider that an apology,’’ he added.

After Amador-Batten got off the plane at the Raleigh-Durham airport on May 20, police told him about the flight attendant’s complaint, spoke to him and then quickly let him go.

He thinks it’s “very possible’’ the attendant singled him out because he’s gay.

“I can’t speak to that man’s heart, and I don’t wear a sticker on my head that says I am gay — but you could possibly look at me and make an assumption,’’ he said. “Somehow he didn’t like what he saw.’’

Amador-Batten said he has been a stay-at-home dad since he and his husband adopted Ben. Before that, he worked as a hairdresser.

He has hired a lawyer and might sue the airline.

United’s recent problems began when it called airport police to drag a passenger off one of its planes in Chicago on April 9 because he refused to give up his seat after being informed the flight had been overbooked.