McCain and Graham said Rice's statements about the Sept. 11 attack on the U.S. Consulate in Benghazi, Libya, should disqualify her from consideration as a potential secretary of state when Hillary Clinton steps down.
U.S. President Barack Obama called the criticism "outrageous" and said he would nominate Rice if he thought she was the best person to succeed Clinton.
When asked by Major Garrett of the National Journal if he agreed with Graham and McCain, Rubio said, "No."
Rubio said Obama has the right to choose whomever he believes will most help the country and that the Senate should wait to respond until it happened.
"I think we need to know the truth," Rubio said. "If we're going to have an honest discussion, I think we need to go in with an open mind."
William Galston, a senior fellow in governance studies at The Brookings Institute, said it was a little surprising to see Rubio publicly disagree with members of his own party so quickly.
"Perhaps Sen. Rubio is more attuned to the desire of the American people for a less confrontational style of politics," Galston said.
Rubio, seen as one of the favorites for the 2016 Republican presidential nomination, was also asked about his recent trip to Iowa. Rubio was headlining a birthday fundraiser for Iowa Gov. Terry Branstad, also a Republican, and some saw the trip as the beginning of the 2016 campaign.
Rubio brushed off the chatter.
"My trip to Iowa has nothing to do with 2016," Rubio said. "I accepted that invitation when I thought Mitt Romney was going to be president of the United States."
Garrett also asked Rubio about how the conservative movement has engaged with immigration policy. Obama received more than 70 percent of Hispanic votes in the Nov. 6 election, with Republican challenger former Gov. Mitt Romney's immigration policy of self-deportation not able to sway Hispanics away from the incumbent.
"Unfortunately, conservatism has done an excellent job of defining what we're against, and not as good a job of defining what we are for," Rubio said. "It's really hard to get people to listen to you on economic growth, on healthcare, on anything else if they think you want to deport their grandmother."
When asked about the upcoming fiscal cliff, Rubio, a Tea Party favorite, said it was "a complete and total congressional creation."
"Sequestration was a dumb idea when it was created and it's a dumb idea now," Rubio said. "That's bipartisanship for you."
The senator said he wouldn't support Obama's plan to end the Bush-era tax cuts because such a move wouldn't reduce the deficit enough to make it worth the risk of the cuts stifling job creation.
"The truth is, if you go forward with doing what the president is proposing, you raise $80 billion in new revenue," Rubio said. "That's 7.5 percent in deficit reduction."
The Washington Ideas Forum is hosted by The Aspen Institute and The Atlantic at the Newseum.