Tillerson, ending a week-long European trip in Warsaw, said that he had secured support from Britain, France and Germany - all parties to the 2015 agreement - to work on the deal that President Donald Trump has warned he will walk away from unless changes are made.
"It's always darkest before the dawn," Tillerson told journalists. "The working groups have already begun to meet on efforts to agree principles, what is the scope of what we attempt to address and also how much we engage Iran on discussions to address these issues," he said.
The nuclear deal gave Iran billions of dollars in sanctions relief in return for curbs on its atomic program.
Trump vowed to stop waiving U.S. sanctions unless the Europeans agreed to strengthen the deal's terms by consenting to a side agreement that would effectively eliminate provisions that allow Iran to gradually resume some advanced atomic work. Trump also wants tighter restrictions on Iran's ballistic missile program.
Iran has rejected any renegotiation.
Tillerson said the nuclear deal was only a "small" part of U.S. policy in the Middle East and Washington was more immediately concerned about other issues including Iran's support for the Houthi rebels in Yemen and its supplying weapons to militias in the region.
"Our work group also is intending to identify areas of greater cooperation (with) Europe to push back on Iran's malign behaviour," he said.
Despite statements from Russia earlier this week that Washington's accusations against Moscow that it and the Syrian army were behind a chemical attack in eastern Ghouta were "unfounded", Tillerson reiterated that ultimately Russia bore responsibility.
"I stand by my comments," he said.
"The chemical weapons ... are being used to hit the civilian population, the most vulnerable - children inside of Syria ... We are holding Russia responsible for addressing this. They are (Bashar al-) Assad's ally."
Russia is providing direct military support in Syria against various rebel groups trying to oust Assad, and giving diplomatic cover in the U.N. Security Council.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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