"As I said in my inauguration speech, if countries like Iran are willing to unclench their fist, they will find an extended hand from us," he said.
"It is very important for us to make sure that we are using all the tools of US power, including diplomacy, in our relationship with Iran."
On Middle East peace, Mr Obama reiterated his administration's support for Israel and its security but also suggested Israelis would have to make some tough choices.
"Ultimately we cannot tell either the Israelis or the Palestinians what is best for them. They are going to have to make some decisions," he said.
"But I do believe the moment is ripe for both sides to realise that the path that they are on is one that is not going to result in prosperity and security for their people. And that instead, it's time to return to the negotiating table."
Asked about verbal attacks made on him in recent videos released by al-Qaeda, Mr Obama responded: "What that tells me is that their ideas are bankrupt."
The BBC's Justin Webb in Washington says that for most of the interview, Mr Obama appeared determined to be emollient and - as he put it repeatedly - respectful, stressing that the US would begin by listening rather than dictating.
As well as meeting Egyptian President Hosni Mubarak, Mr Mitchell is to visit Israel, the West Bank, Jordan, Turkey and Saudi Arabia during a week-long tour, as well as making stops in Europe, said state department spokesman Robert Wood.
CONFLICT IN FIGURES
More than 1,300 Palestinians killed
Thirteen Israelis killed
More than 4,000 buildings destroyed in Gaza, more than 20,000 severely damaged
50,000 Gazans homeless and 400,000 without running water
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