Mayor de Blasio finally acknowledged Tuesday that a spike in street homelessness is a “reality,” but he insisted the city is on top of the issue and would never allow a return to the “bad old days.”

“There is both a perception and a reality problem,” the mayor said on WNYC radio.

“We have a reality today which again makes the previous problems look, in some ways, small.”

Still, de Blasio denounced critics who say the city was backsliding to the “bad old days.”

“The bad old days are gone,” the mayor insisted. “We’ve got to end this madness of talking about the bad old days.”

He said that dealing with more homeless people requires striking a balance between their needs and those of average New Yorkers who encounter them in the streets.

But he vowed the solutions would not come at the expense of public safety.

“I am very devoted to addressing issues of public order,” de Blasio said. “We’re not going to tolerate disorder. We’re not going to tolerate homeless encampments.”

In previous public comments, de Blasio has been reluctant to acknowledge that more people are living on the streets.

On Tuesday, he blamed the growing problem in part on past administrations and slammed former Mayor Rudy Giuliani for chasing homeless people out of the city.

The mayor praised Police Commissioner Bill Bratton for cutting crime dramatically in his first stint as NYPD boss under Giuliani two decades ago.

“Thank God Commissioner Bratton and the NYPD turned the tide from 1994 and onward,” he said.

Giuliani scoffed, “He can’t possibly say that Bratton improved the city without saying I was the mayor who appointed him and I was the mayor who directed him. By the time I left office, the city didn’t have a homeless problem.”

During the interview, host Brian Lehrer took questions from two callers. One, “Margot in Manhattan,” a well-spoken 67-year-old, said she was homeless and living in a convent and asked for a meeting with the mayor to “really speak to him about my experiences.”

De Blasio said he looked forward to the meeting. His office declined to provide further details.