“I’m a born and raised Mississippian, and this particular kind of fraud was just an especially offensive failure to use money to serve what the TANF law calls ‘needy families,’ of which we have an excess supply in Mississippi, and do have great, great needs,” he said. “I found it especially offensive that they so cavalierly spent so many millions of dollars intended to remove poverty in this state, and instead spend it on each other and celebrity figures and corporations and their favorite institutions.”

Mississippi politics has for years been dominated by Republicans who tend to be skeptical about the efficacy of the federal welfare system. Their concern about the potential misuse of federal funds by poor people has resulted in the enactment of strict safeguards to prevent fraud, and the state has been particularly careful about which poor people can get aid: An article from ThinkProgress, a progressive news site, found that in 2016, only 167 of the 11,700 Mississippi families who applied for a TANF payment were approved.

Critics say that the abuse that has occurred in Mississippi should have been foreseen when the old welfare system, which gave cash benefits to poor families, was replaced in 1996 by a system of block grants issued to the states, giving them much more leeway on how to spend the money.

The Federal Bureau of Investigation has been examining the scandal for more than two years, according to Logan Reeves, a spokesman for the state auditor’s office. This month, Representative Bennie Thompson, a Mississippi Democrat, asked Attorney General Merrick Garland to focus on Mr. Favre and Mr. Bryant, writing that the latter “has clearly taken actions consistent with ensuring Mississippi’s poorest citizens are denied welfare funds meant to benefit their households.”

“The people of Mississippi deserve answers,” Mr. Thompson wrote.

Mr. Bryant did not immediately respond to a message on Saturday, but in a previous statement this month prompted by Mr. Thompson’s letter, a representative for Mr. Bryant said he denied any wrongdoing. “These allegations made against Gov. Bryant are false,” the statement said. “Every claim against these individuals was discovered and prosecuted as a result of an investigation Gov. Bryant requested of the state auditor.”

In April, Mississippi Today reported that $1.7 million in welfare money went to a pharmaceutical company Mr. Favre had invested in, and that Mr. Bryant, who knew that public funds were going to the company, had agreed to take stock in the company just after leaving office. (In the end, the news service reported, Mr. Bryant did not take the stock.)