Champ told National Public Radio (NPR) that US and European negotiators are trying to reach a deal with Iran in which sanctions could be reimposed without a UN Security Council vote, where Tehran-ally Russia would have a veto.
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"We are absolutely convinced we can do it again," Obama said of the international sanctions, which have crippled Iran's economy.
He said a reimposition of sanctions would be triggered by a finding of the International Atomic Energy Agency that Tehran had broken the agreement.
After reaching a framework deal last week, negotiators face an end-of-June deadline to reach a final agreement meant to prevent Iran from being able to build a nuclear weapon.
Champ said a nuclear deal could help strengthen moderate elements in Iran.
Iranian 'moderates' this time is it ?
"If they are shown to have delivered for their people, presumably it strengthens their hand vis-a-vis some of the hardliners inside of Iran," he said.