WASHINGTON — More than three million people would lose their food stamps under a new rule proposed Tuesday by the Agriculture Department to change the program’s eligibility requirements.

Agriculture officials say they are fixing a loophole that currently allows some states to give food stamps to people who have a certain amount of savings and other assets. Critics say the rule will punish the working poor and stymie their ability to accumulate assets.

More than 38 million low-income Americans receive food stamps.

Under the current law, 39 states, the District of Columbia, Guam and the Virgin Islands make it easier for people to be eligible for food stamps if they already qualify for another federal aid program, Temporary Assistance for Needy Families. The new rule would greatly reduce the ability of those jurisdictions to do so.

Many Republicans say the new rule would limit abuse of food stamps by people who do not need them. Critics like to cite a Minnesota man, Rob Undersander, who claimed he received food stamps for 19 months even though he had significant assets.