The increases would affect about 712,000 families over the next several years, HUD officials said. Rent hikes would gradually be phased in for tenants based on their income and other provisions that could effectively limit the amount of time some tenants would be allowed to remain in government-funded housing.

“Every year, it takes more money, millions of dollars more, to serve the same number of households,” Mr. Carson told reporters Wednesday in a conference call. “It’s clear from a budget perspective and a human point of view that the current system is unsustainable.”

The proposal, geared at streamlining the agency and cutting the deficit, was intended to start the conversation and should not be regarded as final, Mr. Carson said.

Housing advocates and congressional Democrats immediately condemned it. “What pretends to be a hand up is really a foot in the back,” said Shamus Roller, the executive director of the National Housing Law Project.

On Wednesday, even as Mr. Carson was promoting the plan, department officials acknowledged that it would probably be superseded by a somewhat scaled-back set of rent increases and work requirement proposals House Republicans plan to unveil next month. And the new plan stands little chance of being passed in the Senate, where moderate Republicans like Senator Susan Collins of Maine are likely to reject it.