Richard Rothstein, a spokesman for Veronica Atkins, said Saturday evening that the dinner invitation had been accepted.
The mayor, who a day earlier advised an angry Atkins to "lighten up," didn't deliver an apology himself. Instead, mayoral spokesman Ed Skyler issued a three-sentence statement about the food fight.
"While talking to firefighters about the challenges of losing weight, the mayor made a joke which upset Veronica Atkins," Skyler said. "He never intended to insult her late husband or offend her, and is sorry that has been the result... In order to make it up to Mrs. Atkins, the mayor would like to invite her to a steak dinner - no potatoes."
Rothstein said Atkins "was delighted" with Bloomberg's offer. "She felt it was most gracious," he said.
Rothstein did not know when the two will have dinner together.
The controversial Atkins Diet stresses eating meat, eggs and cheese over high-carbohydrate foods like pasta, potatoes and bread. Bloomberg, during a visit to a Brooklyn firehouse, described Atkins as "fat" and suggested his diet might have led to his death.
Atkins died last year at 72 from head injuries sustained from a fall on an icy sidewalk.
On Friday, an angry Veronica Atkins took the dispute nationwide by appearing on ABC's "Good Morning America" to demand an apology.
"I was very, very hurt," she said. "... And mayor, you did it. Shame on you."
Bloomberg, taping an interview later Friday, said his comments were meant as a joke and there was no need for an apology.