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New York Gov. Andrew Cuomo's directive to send recovering COVID-19 patients to already-vulnerable nursing homes was "clearly a mistake" to be learned from, U.S. Department of Housing and Urban Development (HUD) Secretary Dr. Ben Carson said Friday.

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In an interview on "America's Newsroom" with host Sandra Smith, Carson said that whether or not there were appropriate guidelines in place by the state can be disputed "all day and all night," but using logic could have saved lives.

"Obviously we don't want to take people who have an infectious disease and concentrate them in a place that isn’t prepared to receive them," he said.

FILE - In this Friday, April 17, 2020 file photo, a patient is wheeled out of the Cobble Hill Health Center by emergency medical workers in the Brooklyn borough of New York. The facility has listed dozens of deaths linked to the COVID-19 coronavirus pandemic. In New York state, the nation’s leader in nursing home deaths, the Greater New York Hospital Association lobbying group wrote the first draft of an emergency declaration making it the only state with protection from both civil lawsuits and criminal prosecution arising from the pandemic, with the order signed by Democratic Gov. Andrew Cuomo. (AP Photo/John Minchillo) (AP Photo/John Minchillo)

A new report released Friday by The Associated Press revealed that more than 4,300 recovering coronavirus patients had been sent to New York's nursing homes under the March health order. While Cuomo has since amended this policy -- and, more recently, ordered that all nursing home staff be testing for the virus biweekly -- the death toll in homes and long-term care facilities has exceeded 5,000 people.

On Wednesday, Cuomo brushed off calls for the Justice Department (DOJ) to open an investigation into the massive number of deaths during the pandemic, shifting the blame toward guidelines from the Trump administration and the Centers for Disease Control and Prevention (CDC).

Cuomo, a Democrat, has also announced he is conducting his own inquiry under the leadership of State Attorney General Letitia James, also a Democrat.

“This is a political season, I get it,” he said. “I’m not going to get into the political back-and-forth, but anyone who wants to ask why did the state do that with COVID patients in nursing homes, it’s because the state followed President Trump’s CDC guidance.”

Cuomo added: “They should ask President Trump. I think that will stop the conversation.”

"Of course you're not supposed to discriminate against anybody. All the federal guidelines say that about everything. That's a ridiculous argument," Carson responded.

"Obviously, you want to accept people if you have provisions and have taken the appropriate safeguards, but you just don’t say, ‘Okay, let's bring somebody with tuberculosis in here because we are not supposed to discriminate against them’ without having prepared for that."

"That makes absolutely no sense whatsoever to a Republican, a Democrat or anybody with a brain," he added.

Smith asked the secretary whether or not he thought there is a need for a federal probe into the nursing home deaths in the state.

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"Well, it would be good to make sure that we know what the weaknesses were so that we could correct them," Carson told Smith. "I'm not sure that it would be useful to put people in jail and to compound a tragedy that has already occurred."

Fox News’ Marisa Schultz, Andrew O'Reilly, and Gregg Re contributed to this report.