In even colder climes to the north of New York City, Stephanie A. Miner, the mayor of Syracuse, called the governor’s action “an admirable goal.” But she, too, questioned forcibly removing homeless people from the streets, something she likened to “criminalizing homelessness.”

“Sheltering people means you have to build relationships, because a lot of them have mental health issues or substance abuse issues,” said Ms. Miner, a Democrat who has frequently criticized Mr. Cuomo. “In order to enforce this executive order, we’re going to have to have the police do it. And that goes against what we’ve been doing in building those relationships.”

The governor’s office said on Monday that the plan would be flexible, and that assessments would be made of each individual, as required by the Mental Hygiene Law, and people will not be held against their will, unless they were deemed mentally ill and a danger to themselves or others. Administration officials also continued to offer assistance and guidance on the order. The State Police could be used in some rural areas, though homelessness is primarily an urban problem.

In an interview, Alphonso B. David, the governor’s chief counsel, said the order “is saying to the municipalities that they must engage with their homeless population.”

“It’s not intended to be punitive; it’s intended to save lives,” Mr. David said.

While the executive order is “a directive,” Mr. David said, “an administrative policy is just that: It’s not an edict, and it’s subject to interpretation.”

The governor’s remarks earlier on Monday also cast the order — which invoked the State Constitution and powers usually employed to address natural and man-made disasters — as an “outreach effort.” He assigned much of the blame for street homelessness in New York City — where several thousand people permanently live out of doors — at what he repeatedly said was the city’s lack of an adequate shelter system.

“Most people don’t want to freeze to death; they want to go into the shelter. It’s called human instinct,” Mr. Cuomo said, adding that he planned to initiate a review of conditions in the city’s shelter system. “The simple answer is we need to get people off the streets. We need a safe, clean and decent shelter system to do that. And as we stand here today, that is a major obstacle.”