Tillerson, in an interview on Fox News, said the so-called sunset clauses, under which some of the 2015 deal's restrictions on Iran's nuclear program expire over time, were of particular concern.
"If we're going to stick with the Iran deal there has to be changes made to it. The sunset provisions simply is not a sensible way forward," Tillerson said. "It's just simply ... kicking the can down the road again for someone in the future to have to deal with."
Tillerson's comments come after Prime Minister Benjamin Netanyahu delivered his address to the United Nations General Assembly, during which he launched into a tirade against the clause.
Blasting the clause for permitting the lifitng of restrictions on Iran not by dint of an improvement in its "behavior" but simply "by a mere change in the calendar," the Israeli premier said that "when that sunset comes, a dark shadow will be cast over the entire Middle East and the world, because Iran will then be free to enrich uranium on an industrial scale, placing it on the threshold of a massive arsenal of nuclear weapons."
Without mentioning it specifically, President Donald Trump also seemed to have taken aim at the sunset clause during his speech to the General Assembly.
"We cannot abide by an agreement if it provides cover for the eventual construction of a nuclear program,” Trump said after denouncing the deal as an "embarrassment."