The Brooklyn District Attorney’s Office is stalling for time in the crumbling case against five teens accused of gang rape — as the alleged victim’s dad was questioned by police again on Thursday evening, law enforcement sources told The Post.

Prosecutors had until Friday to secure a grand jury indictment, otherwise the teen suspects could be released without bail. But they won’t make that deadline, so 17-year-old Onandi Brown was to be released from jail on Thursday, law enforcement sources said.

“Because we are determined to get to the truth about what happened in that park, we need more time to investigate this complex case and gather more evidence. So, therefore, we have consented to the defendants’ release,” said Brooklyn District Attorney Ken Thompson in a statement.

Three of the teens had already posted bail. The fifth suspect, 15-year-old Shaquell Cooper, will not be released from jail because he’s still being held on a different case from October, in which he allegedly punched a person.

The DA’s office now has six months to build a case for a grand jury. The Post first reported on Thursday that the case was falling apart because of credibility issues with the alleged victim’s father.

Onandi’s attorney, Spencer Leeds, said the DA “did a very decent thing that, because Onandi was still in jail, he agreed to release him today.

“We believe that after a full and fair investigation is completed, my client will be exonerated,” he added.

Police Commissioner Bill Bratton said Thursday that the DA’s office is continuing to conduct interviews as they try to piece together exactly what happened.

“The first story is never the last story … we’ll just have to, over the next several days working with the DA’s office, go where the truth takes us and try to get there as quickly as we can,” Bratton said.

Meanwhile, the father of the alleged victim was brought in by detectives for another round of questioning Thursday night — but he has not been charged with a crime, law enforcement sources said.

He insisted earlier in the day that he wasn’t having sex with his daughter when the five teenage suspects showed up, as two of the young men have claimed.

“They’re just trying to get out of the thing they did,” the dad told The Post as he walked from his Brooklyn home to a nearby deli, where he picked up two beers.

Two of the five teens arrested for the alleged rape insist they had consensual sex with the young woman in the Osborn Playground in Brownsville at about 9 p.m. last Thursday.

They also claim her drunk father was having sex with her when they came upon them, an allegation that cops are looking into, according to law enforcement sources.

But the victim’s dad is standing by his story that the teens held them up at gunpoint before he ran away from the scene.

“I want them to rot in jail,” he said.

When asked point-blank if he was having sex with his daughter, he responded, “No.” As for clearing his name, he insisted his name is “already clear.”

Sources said the cops have the dad’s DNA, which is standard procedure in a case like this.

Bratton said Thursday that cellphone footage taken just before the alleged rape is a “significant piece of evidence.”

“I believe it’s 9 to 11 seconds,” the top cop said. “I believe it’s been retrieved from one of the cellphones carried by one of the five young men that are being investigated in this matter.”

Relatives of the five teenage suspects said the video shows the 18-year-old woman with her pants down as her father stands nearby.

In a short clip viewed by The Post, a young woman sits on the ground grinning, while young men laugh in the background.

At one point, a teen asks an older man, “Can we have some of that?,” law enforcement sources said.

A young man then tells the girl, “You said, ‘Yeah.’ That’s what I’m saying, it’s lit [OK], like you know what I mean? I could tell you a freak,” according to sources.

The five teens have been charged with rape, forcible compulsion, criminal sex act and sex abuse.