Appearing on CNN earlier Thursday, Sununu said he wondered whether Powell had "a slightly different reason for preferring President Obama."
Host Piers Morgan asked what reason that would be. Sununu said: "Well, I think when you have somebody of your own race that you're proud of being president of the United States, I applaud Colin for standing with him."
Sununu served as White House chief of staff under President George H.W. Bush. Powell is a retired four-star Army general who was secretary of state for President George W. Bush.
Obama, asked Friday about Sununu's comments, said: "I'll let Gen. Powell's statements stand for themselves."
The president told conservative radio host Michael Smerconish that few would question Powell's credibility or patriotism. "And so any suggestion that Gen. Powell would make such a profound statement in such an important election based on anything [that isn't] best for America doesn't make much sense."
Powell endorsed Obama Wednesday on CBS This Morning, saying the president got the United States out of Iraq, has laid out a plan for leaving Afghanistan, "and didn't get us into any new wars."
He praised Obama's economic performance, saying that while difficult choices are ahead on taxes, spending and budgetary policies, "steadily, I think we've begun to come out of the dive, and we're gaining altitude."
Powell also endorsed Obama during the 2008 campaign.