The deal will take effect unless Congress blocks it, and Republicans in control of the House and Senate have made clear they intend to try to do so in September.
Kerry said that when the negotiations began, experts calculated that it would take Iran only two to three months to produce enough material for a bomb, the so-called breakout time.
If the deal is denied, he warned, it would signal a "great, big, green light" for Iran to speed up its nuclear programme without any transparency or monitoring by the international community.