"We have a national interest in trying to put the nuclear problem back in the box that it was in the JCPOA," Blinken told a joint news conference with his French counterpart Jean-Yves Le Drian in Paris, using the formal name of the nuclear agreement.
The United States abandoned the deal under former president Donald Trump in 2018 and Iran responded by dropping some of its terms. The administration of US President Joe Biden wants to rejoin the accord, but Tehran and Washington have yet to agree which side should take what steps, and when.
Blinken and Le Drian said that one key Biden promise – to rejoin to the accord – was at risk if Iran does not make concessions during talks that have been going on for months in Vienna.
Blinken said that the United States still had "serious differences" with Iran.
"There will come a point, yes, where it will be very hard to return back to the standards set by the JCPOA," he told reporters, according to AFP.
"We haven't reached that point – I can't put a date on it – but it's something that we're conscious of."
"We are only going to reach an agreement with Iran if it honors its obligations under the JCPOA, and we are just not there yet," he said, according to Reuters.
Iran says its reduction of commitments to the JCPOA are in compliance with articles 26 and 36 of the deal that cover its legal rights.
France – which like Britain, Germany, Russia and China had stayed in the accord despite pressure from Trump – urged Iran to make “difficult” decisions.
"We expect the Iranian authorities to take the final decisions – no doubt difficult ones – which will allow the negotiations to be concluded," Le Drian said at the joint news conference.
Iran insists that all sanctions imposed by Trump need to be removed before the US reenters the deal, pointing to the promises of economic relief under the accord.
The Biden administration says it is ready to lift economic sanctions related to nuclear work as laid out by the JCPOA – but that it will keep other sanctions, including over human rights and Iran's support to resistance groups in the Middle East.
One of Iran's moves to reduce compliance was a decision to end extra monitoring of its nuclear sites by the International Atomic Energy Agency (IAEA) in February. The inspections were extended twice by temporary deals, the last of which ended this week.