US and Iranian officials are scheduled to begin indirect talks in Vienna, with European officials expected to act as intermediaries, to try to revive the 2015 pact under which economic sanctions on Iran were eased in return for curbs on its nuclear programme.
Iran has ruled out direct discussions and Mr Price said Washington did not expect any "at present" but was open to the possibility.
The US special envoy for Iran, Rob Malley, a veteran of the Clinton and Obama administrations, will lead the US delegation in Vienna, where the pact was originally reached in 2015.
The agreement was struck by Iran and six major powers: Britain, China, France, Germany, Russia and the US.