"But we believe this is a healthy step forward", Price said in a statement.
Iranian Foreign Minister Javad Zarif said there would be no direct meeting between Iran and the United States as signatories gather Tuesday.
It is unclear how long the meetings will last for, the official said.
On Friday, the Joint Commission of the Joint Comprehensive Plan of Action, the formal name for the nuclear deal, met virtually without the United States and confirmed another meeting will take place next week in Vienna.
The Iranians have called for the U.S.to lift economic sanctions, which were reimposed by former President Donald Trump after he unilaterally quit the nuclear deal in May 2018.
The U.S.is speaking to partners "about the best way to achieve this, including through a series of initial mutual steps", he added.
Price said the talks would be structured around working groups the European Union is going to form with the remaining participants in the nuclear agreement, including Iran.
Senior officials from the governments of Iran, France, the UK, Germany, Russia, China, the United States and the European Union will all be in the same city.
The State Department also confirmed Thursday that the USA had granted Iraq an extension to a sanctions waiver allowing it to import Iranian gas. "In this context, the coordinator will also intensify separate contacts in Vienna with all JCPOA participants and the United States".
He added for good measure: "No Iran-US meeting".
But Tehran says Washington has to lift worldwide sanctions that were reimposed by Trump before it will make any moves to get back in line, and is refusing to hold direct negotiations with the US.
Israeli officials, including Prime Minister Benjamin Netanyahu, have already begun voicing opposition to the Biden administration's desire to rejoin the deal, putting Jerusalem and Washington at odds on the issue.
Russia's ambassador to global organizations in Vienna, Mikhail Ulyanov, tweeted that Friday's session went well and the parties were prepared to talk further.
While U.S. officials will be present in Vienna, Iran as yet seems unwilling to engage directly with Washington.
Iran has said that before it resumes compliance with the deal, the US needs to return to its own obligations under the deal by dropping the sanctions.
The top Iranian diplomat also emphasised that the goal of the Vienna negotiations is to "rapidly finalise sanction-lifting and nuclear measures for [a] choreographed removal of all sanctions, followed by Iran ceasing [its] remedial measures".