PORTLAND — If Gov. Paul LePage follows through on this threat to cede Maine’s administration of the federal food stamp program, the federal agricultural agency said it can’t run it, due to a lack of authority and funding.

Maine unsuccessfully applied for a waiver to ban using food stamps for buying sugary drinks and candy. If the state institutes the ban outright, as LePage has suggested, Maine would risk losing federal funding, according to U.S. Department of Agriculture spokesman Matt Herrick.

The agency — which has never granted such a waiver — says Maine has yet to provide details about evaluating the ban’s impact on the state’s high obesity rates.

LePage, a Republican, wrote to the USDA that he’ll seek unilateral reform or cease Maine’s administration of food stamps.

The governor defended the ban as a common-sense measure standing up to the powerful food lobby. He said he’s not “naive enough” to think Maine can satisfy the agency’s concerns.

The governor’s spokespeople didn’t respond to questions about LePage’s letter.

According to the USDA, about 100,000 Maine households receive federal Supplemental Nutritional Assistance Program benefits.

Though food banks report significant food insecurity in Maine, participation in food stamps has dropped from about 230,000 Maine recipients in 2014 to roughly 190,000 participants currently.

LePage criticized the USDA’s assertion that Maine must work on application backlogs, error rates and staffing shortages.

Herrick said that as of May, Maine had about 2,000 pending food stamps applications, with more than 300 a month old. He added that though Maine’s Department of Health and Human Services has used staff overtime to address backlog concerns, it stopped doing so in February.

“Since that date, timeliness performance has deteriorated,” Herrick said.

The DHHS didn’t immediately respond to request for comment.

States like Minnesota, and cities such as New York City, have sought banning food stamps from buying sugary food but have faced similar waiver denials as well as disagreements about what constitutes junk food.

The USDA wants states to adopt programs that provide incentives for recipients to eat healthy, like allowing food stamps at farmer’s markets.