"I want to absolutely clear to with everybody: We are not yet where we need to be on several of the most critical issues," Kerry told reporters outside the 19th-century Viennese palace that has hosted the negotiations.
World powers and Iran are hoping to clinch a deal by Tuesday, setting a decade of restrictions on Iran's nuclear program and granting Iran significant relief from international sanctions.
"It is now time to see whether or not we are able to close an agreement," Kerry said, after hobbling on crutches through 97-degree heat to a podium set up in a city square.
While "genuine progress" had been made and the sides "have never been closer, at this point, this negotiation could go either way. If the hard choices get made in the next couple of days, and made quickly, we could get an agreement this week," Kerry said.
The talks had appeared to be moving forward. Yesterday, diplomats reported tentative agreement on the speed and scope of sanctions relief for Iran in the accord, even as issues such as inspection guidelines and limits on Iran's nuclear research and development remained contentious.
Tuesday's deadline is the latest that has been set for a comprehensive pact that would replace the interim deal world powers and Iran reached in November 2013.
That package was extended three times, most recently on June 30, and Kerry appeared to be partly addressing critics of the diplomacy in the US who've argued that President Barack Obama's administration has been too conciliatory over the course of the negotiations.
Speaking at the same time as Sunday news shows aired in the US, Kerry said that "if we don't have a deal, if there's absolute intransience with the things that are important, President Obama has always said we would walk away.
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