But he argued that the best possible available agreement with Tehran was likely to be better than the alternatives, and it was therefore imperative to try to secure one.
Obama, speaking at the Brookings Institution's Saban Forum in Washington, said a deal was possible that included enough verification safeguards to assure foreign powers Tehran could not build a nuclear bomb.
He indicated that could include a very "modest" option for Iran to enrich uranium as part of a peaceful nuclear program under intense scrutiny by outside observers that would ensure Tehran was kept from "breakout" capacity needed to race to build an atomic weapon.
"But I want to make sure everybody understands it -- that particular option is not available, so as a consequence, what we have to do is make a decision, as to given the options available, what is the best way for us to assure Iran does not get a nuclear weapon?"
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Obama noted likely criticism from Israel of any final deal that did not eliminate all of Iran's nuclear infrastructure as he laid out a pragmatic case for the negotiations.
But he added: "I think we have to be more realistic and ask ourselves what puts us in a strong position to assure ourselves that Iran is not having a nuclear weapon."
Obama also made clear that the interim deal reached in Geneva last month between Iran and world powers did not grant Iran a "right to enrich," despite such interpretations of the deal by some top Iranian officials.
"We can envision a comprehensive agreement that involves extraordinary constraints and verification mechanisms and intrusive inspections but that permits Iran to have a peaceful nuclear program," Obama said.
"Now, you'll hear arguments including potentially from the (Israeli Prime Minister Benjamin Netanyahu) that says we can't accept any enrichment on Iranian soil, period, full stop, end of conversation," Obama said as he warned that such solutions of "an ideal world" were not within reach.