Gates accepted Obama's invitation Friday night on The Root, the Web site Gates runs. In a statement posted on the Web site, Gates said that he and Obama agreed that his experience could be used as "a teaching moment," and, "if meeting Sgt. Crowley for a beer with the president will further that end, then I would be happy to oblige."
"If my experience leads to the lessening of the occurrence of racial profiling, then I would find that enormously gratifying," Gates wrote. "Because, in the end, this is not about me at all; it is about the creation of a society in which 'equal justice before law' is a lived reality."
Debate continues, however, on whether Obama went too far in his involvement in the controversial case.
Brazile said on "This Week" that the president, "having had the experience of many black men in this country," may have been using "his heart over his head" when he said Cambridge police acted "stupidly," a comment that provoked criticism from Cambridge police, among others.
Still, Brazile said, Obama was right to speak out.
"I think the president was trying to raise a much larger issue, but unfortunately his word choice got in the way," she said.
But ABC News political analyst George Will said the president had no business getting involved in the matter in the first place.
"Presidents should understand that some things are not any of their business," he said, "such as local police disputes in Cambridge, Mass."
Obama, he said, is "ubiquitous."
"Somewhere between the remoteness of Charles de Gaulle and the ubiquity of Barack Obama, there's a happy medium," Will said.
With reports from ABC News' Yunji de Nies.