“Children have been harmed as a result of NYCHA’s failures,” an 80-page federal complaint accompanying the decree stated — a departure from de Blasio’s assertion months ago that “Thank God there has not been harm done to any child because of the mistakes that have been made.”

But he also acknowledged during a City Hall press conference on Monday that the deal allowed him to avoid a trial following a three-year investigation by the U.S. Attorney’s Office in Manhattan.

“A trial [was] an option. We made a choice. Did we consider the options? Yes. We thought this was the right thing,” de Blasio said.

He did not dispute the potential of criminal charges, following findings that top housing authority officials not only put residents in harm’s way, but also orchestrated a cover-up that involved lying to federal officials for years and devising a “how-to” guide for deceiving inspectors.

“The conversations that I was part of were all about fixing the underlying problems,” he said, when asked if criminal charges against anyone at the housing authority or in City Hall were a possibility. “The U.S. Attorney, of course, reserves their rights and I understand that. But all we talked about was fixing the structural problems. I can’t conjecture on anything else.”

U.S. Attorney for the Southern District of New York, Geoffrey Berman, declined to say why the government did not press charges but said that possibility remains an option.

“When an entity like NYCHA enters into a consent decree like this, it is inconsistent to bring a criminal charge. The object is to reform NYCHA, not to bring a criminal charge against NYCHA, but … we have complete flexibility with respect to criminal investigation charges for individuals,” Berman said at his own press conference in Lower Manhattan.

Combined with federal and state aid, the housing authority will be getting $4 billion over four years to fix its deteriorating buildings.

The money pales in comparison to NYCHA’s outstanding capital needs — at least $25 billion over five years, according to a report the city has delayed making public for months.

“Today marks the beginning of the end of this nightmare for NYCHA residents,” Berman said.

He said he was “outraged” when he learned about the conditions in public housing. “My blood was boiling,” he added.

At least 19 children who had lead poisoning between 2010 and 2016 were exposed to lead paint in their NYCHA apartments, according to the complaint.

“These 19 children are at risk of lifelong neurological problems,” it reads. “But the 19 cases understate the true extent of lead poisoning likely to have been caused by crumbling lead paint at NYCHA.”

That was just one of the dangers.

“Mold grows unchecked at many NYCHA developments, often on a large scale. Across the city, residents are provided inadequate heat in winter, leading to frigid apartment temperatures,” the complaint reads. “Pests and vermin infestations are common, and as senior New York City officials have acknowledged, NYCHA ‘has no idea how to handle rats.’”

Prosecutors described broken elevators that trap elderly and disabled residents in their apartments or force them to sleep in lobbies.

The agency lied to federal officials for years, both before de Blasio took office and throughout his first term.

“Year after year, NYCHA falsely certified that it was in compliance with lead paint regulations when it was not,” Berman said.

He accused the authority of using “every trick in the book” to hide building code violations and falsifying reports to the federal department of Housing and Urban Development.

“Without injunctive relief, NYCHA’s deceptive conduct and its ongoing effects will continue,” the complaint reads.

Shola Olatoye, who ran the housing authority during de Blasio’s first term, resigned in April. She and de Blasio both described her departure as voluntary, and the mayor continued to defend her on Monday. Olatoye declined to comment.

The mayor is still searching for a permanent chair as government veteran Stanley Brezenoff fills in temporarily.

Four housing authority employees, including general manager Michael Kelly, were forced to resign following a report from the city Department of Investigation in November about lapsed lead paint inspections. The mayor warned Monday that more staff discipline may be coming.

“We will do the work of weeding out anyone who should not be here or anyone who’s done something wrong,” he said.

He shielded his deputy mayor for housing and economic development, Alicia Glen, from answering a question posed to her about her knowledge of falsified reports.

The mayor characteristically blamed prior administrations, Gov. Andrew Cuomo and the federal government for short-changing the agency long before he took office.

“My administration and I will offer an apology, but the administrations before me should offer an apology too,” he said.

A spokesman for former Mayor Michael Bloomberg declined to comment or answer a question about falsified reports the housing authority submitted to federal officials in 2012 and 2013.

The agreement urges the state to turn over $550 million it has budgeted in recent years for the housing authority, saying the money and the authority to do design and construction for capital repairs simultaneously “are important to the success of this consent decree.”

Cuomo seized on problems at the housing authority in March, visiting dilapidated buildings and holding press conferences to highlight the roaches, broken boilers and crumbling walls he encountered.

On Monday he said he would forgo his plans for a separate state monitor to oversee spending at NYCHA.

“I’ve never seen a city be penalized this way before, where they have to pay billions and billions of dollars and the federal government pays nothing,” he said at a press conference. “It’s an admission of their culpability.”

One of the tenant representatives invited to attend the mayor’s press conference mentioned Cuomo, unprompted, three times when a reporter asked about the federal complaint and the city’s management of the housing authority.

“Honestly, I don’t believe the governor really does care,” resident association president Nancy Ortiz said. “I believe public housing came on his radar because it’s an election year. He’s never toured public housing in the past. Why now?”

Cuomo campaign spokeswoman Lis Smith took to Twitter to chastise the mayor’s management of the authority.

“Another day, another excuse from @billdeblasio about his failed leadership of NYCHA,” she said in a tweet. “While the mayor was covering up the plight of NYCHA residents, @AndrewCuomo was shining a light on it & demanding accountability.”