The cable network's conservative commentators regularly criticize the president in harsh terms and the outlet often zeroes in on stories that cast the White House in a negative light.
"What our advisers have simply said is that we are going to take media as it comes," Mr. Obama said. "And if media is operating, basically, as a talk radio format, then that's one thing. And if it's operating as a news outlet, then that's another."
"But it's not something I'm losing a lot of sleep over," he added.
The president argued that the controversy over the White House's recent criticism of Fox News – first voiced by White House communications director Anita Dunn, who called Fox News "a wing of the Republican Party," and later by White House Chief of Staff Rahm Emanuel and Senior Adviser David Axelrod – is largely a Washington phenomenon.
"I think the American people are a lot more interested in what we're doing to create jobs or how we're handling the situation in Afghanistan," he said.
On that front, the president told Guthrie that his administration may decide on its Afghanistan strategy before the runoff election between incumbent president Hamid Karzai and challenger Abdullah Abdullah on November 7th.
"I think it is entirely possible that we have a strategy formulated before a runoff is determined, we may not announce it," he said.
Mr. Obama also talked about the relationship between men and women, urging young husbands to "understand the incredible juggling act that moms are going through every day."
Before he became president, he said, there was "a lot of negotiations" between Mr. Obama and his wife Michelle.
The president also joked that he is "surrounded" in an all-female household, with the exception of the family dog. "It's me and Bo," he said.
"What I've tried to do was to learn to be thoughtful enough, and introspective enough, that I wasn't always having to be told that things were unfair," said the president. "And then once in awhile, I'd actually voluntarily say, 'You know what? Let me relieve this burden on you. Let me make some sacrifices, in terms of how I'm using my time.' But, you know, there's no doubt that our family, like a lot of families out there were ones in which the men are still a little obtuse about this stuff."
He said he still needs "to be knocked across the head every once in awhile, in terms of, you know, making sure that everybody is treated fairly."
"The truth is, Michelle still had to make sacrifices of the sort that I did not have to make," he added.
The president was also asked about a basketball game he recently held at the White House where all the participants were men. He called criticism of the guest list "bunk" and said the invitees had simply been the regulars at the House of Representatives' pick-up game.
"I don't know if there are women who - were Members of Congress who play basketball on a regular basis," Mr. Obama said. "I don't think there are. You know, I don't think sends any kind of message or signal whatsoever."