There is no shortage of evidence to prove that Mr. Trump is wrong about that. The United States Interagency Council on Homelessness — a coalition of 19 federal agencies — has been producing the national strategic plan to prevent and end homelessness since 1987. An interactive map on the council’s website shows state-by-state homeless numbers.

A report released in December by the Department of Housing and Urban Development documented the longstanding trends. Over all, the rate grew by 0.3 percent in 2018, leaving 552,830 people without stable living conditions despite a booming economy that Mr. Trump frequently takes credit for. The report noted that high rents in some big cities caused higher spikes in homelessness.

As president, Mr. Trump has given little indication that homelessness in America is a priority for his administration.

But during the Fox News interview, he said he was “looking very seriously” at how to deal with cities that he said were overrun with mentally ill and “sick” homeless people who ruin life for others who live and work there.

“The people living there are living in hell,” Mr. Trump said. “Some of them have mental problems where they don’t even know they are living that way. In fact, perhaps they like living that way. They can’t do that. We can’t ruin our cities.