In a rare show of flexibility for an administration that has usually pressed forward with regulatory changes despite protests, the public comment period will be reopened for 14 days so the public can weigh in on the second analysis. Almost 130,000 public comments have already been received, most of them in strong opposition to the rule change.

That is not likely to change.

“The additional analysis is woefully inadequate at addressing the concerns raised by tens of thousands of commenters and does nothing to mitigate the harm to low-income children from the underlying proposal,” said Zoe Neuberger, a senior policy analyst at the liberal Center on Budget and Policy Priorities.

The Trump administration has tried three times now to reduce funding for or limit access to the Supplemental Nutrition Assistance Program, or the food assistance program. But this is the first time the administration has accommodated opponents to a rule amid criticism.

The department aims to 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. It also wants to prevent households with more than $2,250 in assets, or $3,500 for a household with a disabled adult, from receiving food stamps. Republicans often point to a millionaire in Minnesota, Rob Undersander, who said he received food stamps for 19 months even though he had significant assets.

“While this is likely not common, it is emblematic of a larger problem in these programs,” Representative James R. Comer, Republican of Kentucky, said during a recent hearing on the proposed change.