The tentative rapprochement between the US and Iran that began in secret in 2011 was said to be feared by the Saudis , and , during the run up to the widely welcomed deal on Iran 's nuclear programme that capped the first stage of US – Iranian détente , Robert Jordan , who was U.S. ambassador to Riyadh from 2001 to 2003 , said " Saudis ' worst nightmare would be the [ Obama administration striking a grand bargain with Iran . "