European mediators last month appeared to make progress in restoring the 2015 accord as Iran largely agreed to a proposed final text.

But optimism dimmed when the United States sent a reply, to which Iran in turn responded.

"In past weeks, we've closed some gaps. Iran has moved away from some extraneous demands -- demands unrelated to the JCPOA itself," Blinken told reporters, using the acronym for the 2015 Joint Comprehensive Plan of Action.

"However, the latest response takes us backwards. And we're not about to agree to a deal that doesn't meet our bottom-line requirements," he said.

"If we conclude a deal, it's only because it will advance our national security."

President Joe Biden supports restoring the agreement, under which Iran will enjoy sanctions relief and again be able to sell its oil worldwide in return for tough restrictions on its nuclear programme.

Biden's predecessor Donald Trump trashed the agreement and instead imposed sweeping new sanctions.

Diplomats say Iran has dropped a demand that Biden lift Trump's designation of the elite Revolutionary Guards as a terrorist group, a key sticking point.

But disputes include Iran's insistence that the UN nuclear watchdog close a probe into three undeclared sites suspected in previous nuclear work.

While in Brussels, Blinken met virtually with his counterparts from Britain, France and Germany, which remain in the accord.