"Even with the nuclear deal we recognise collectively that we continue to have serious concerns about Iranian behaviour", Obama said at the close of a summit in the Saudi capital with the six-nation Gulf Cooperation Council.
He referred to Iran's "destabilising activities" in the region but said: "None of our nations have an interest in conflict with Iran."
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Differences over relations with Iran are at the heart of tensions between Sunni Gulf nations and Washington.
Gulf states are concerned about what they see as Obama's moves towards closer ties with their Shiite arch-rival, fearing that Tehran will be emboldened to seek a bigger regional role after the lifting of sanctions under its landmark nuclear deal with major powers led by the United States.
Saudi Arabia and its Gulf neighbours accuse Iran of widespread interference throughout the region, where they support opposite sides in conflicts in Yemen and Syria.