Under the rule, effective April 1, 2020, an area eligible for a waiver would have to have a 24-month average unemployment rate that is not only 20 percent above the national average but also at least 6 percent.

Anti-poverty groups said the administration’s focus on the unemployment rate was misleading.

“The overall unemployment rate is really a measure of the whole labor market and not people without a high school diploma who are incredibly poor and may lack transportation,” said Stacy Dean, the vice president for food assistance policy at the liberal Center on Budget and Policy Priorities. “We’re talking about a different group who just face a very different labor market.”

The rule is the first of three Agriculture Department efforts to scale back the food stamp program, and so far, Trump administration officials appear unmoved by the protests flooding in. More than 140,000 public comments were submitted on the rule that was made final on Wednesday, and they were overwhelmingly negative.

“The Trump administration is driving the vulnerable into hunger just as the Christmas season approaches,” Senator Chuck Schumer of New York, the Democratic leader, said on Wednesday. “It is heartless. It is cruel. It exposes a deep and shameful cruelness and hypocrisy in this administration.”

The department has also proposed a rule that would close what it calls a loophole that allows people with incomes up to 200 percent of the poverty level — about $50,000 for a family of four — to receive food stamps. The rule would also prevent households with more than $2,250 in assets, or $3,500 for a household with a disabled adult, from receiving food stamps. Those changes would strip nearly three million people of their benefits, the department said, and nearly one million children would lose automatic eligibility for free or reduced-price school meals. The proposal received 75,000 public comments, which were overwhelmingly negative.