Hundreds of ticket holders for a Jay-Z concert were stuck outside Yankee Stadium in New York for hours on Sunday night, waiting to be let in for a performance that was delayed several hours.

When the rapper eventually took the stage after midnight, he apologized. The doors to the stadium had been closed for concertgoers’ safety because some people had tried to rush the gates, he said.

“There’s 10,000 people outside,” he said, according to videos posted on social media. “I don’t want to start the music and people get trampled.”

In a joint statement, the Yankees, Roc Nation and Live Nation organizations said that hundreds of people in large groups, without tickets, stormed various entrances of the stadium and in some cases, breached security.

“As a result, gates at all entrances of the Stadium were closed for an extended period of time,” the statement said. “With the thoughtful guidance of the NYPD, gates were reopened cautiously and carefully to ensure the safety of those inside and outside.”

The New York Police Department deferred to the joint statement when asked for information about the incident.

Before the concert began, some fans outside the stadium in the Bronx had expressed frustration and anger, saying they had waited more than four hours. Doors for the show opened at 6 p.m., and the scheduled start time was 8 p.m., according to a social media post by Yankee Stadium. It was the last of Jay-Z’s three concerts in New York.

Stef Seger, 41, and her 11-year-old son, Eli Mize, of Kansas City, Mo., flew to New York late Saturday to see their first Jay-Z show. Around 8:20 p.m., just as they arrived outside Gate 4, on the western side of the stadium, security guards locked the doors, Ms. Seger said.

“They said they had to close it because people were rushing the gates,” she said.

Just after 12:30 a.m., Ms. Seger said she saw some fans being let through. “We just kept holding out hope,” she said. “We were almost going to leave. But people kept saying it’s going to happen.”

Tony Cardy, 50, who had arrived just after 8 p.m. with his partner, said the venue staff had not communicated the situation to ticket holders. But for him, leaving was not an option.

“You know how much we paid for these tickets?” Mr. Cardy said. (They were $1,200 each.)

Around 12:30 a.m., police officers surrounded the gates as they were propped open, and a crowd pushed forward through the metal detectors. Several officers stood in front of the entrances with their arms in the air, signaling the crowd to stay back. Many fans continued to push ahead, some shouting, “Let us in!”

As fans began to trickle into the stadium, Chanelle Green, 40, of West Orange, N.J., was still outside, hoping she would also soon make it in.

“It was one of those things where you’ve invested so much time that turning around didn’t make sense,” she said.

“I’m a huge fan,” she added. “His whole catalog takes up the majority of my childhood. That’s why I’m still here.”