"There still remain some difficult issues," Kerry told a CNN reporter in his luxury lakeside hotel in the Swiss town of Lausanne.
"We are working very hard to work those through. We are working late into the night and obviously into tomorrow."
Global powers are racing against the clock to nail down the final pieces of a framework deal aimed at stopping Iran from obtaining a nuclear bomb by tomorrow midnight deadline.
He will only return if there is a "realistic" chance of a deal, his spokeswoman said earlier.
Kerry said there was "a little more light ... Today, but there are still some tricky issues. Everyone knows the meaning of tomorrow. "
State Department acting spokeswoman Marie Harf appealed to the Iranians to help overcome the last hurdles. "It's sort of time to see whether they can make these decisions."
German Foreign Minister Frank-Walter Steinmeier said major points of contention were Iran's "very ambitious" demands once a first "phase" of a deal lasting around 10 years expires.
Lavrov and his counterparts from the United States, China, Britain, France and Germany are trying to pin down the outlines of a deal which will then be fleshed out with technical annexes by June 30.
They want Iran to scale back its nuclear programme to give the world ample notice of any dash to make the bomb and end a crisis that has threatened to escalate dangerously for 12 years.
The diplomatically isolated Islamic republic denies wanting atomic weapons and is calling for the lifting of sanctions that have strangled its lifeblood oil exports and its access to the global financial system.
Global powers only want a gradual easing of the sanctions to ensure they can be snapped back into place if Iran reneges on the deal.
The threat of new US sanctions, and domestic pressure on Iranian President Hassan Rouhani for his attempts at rapprochement with the West, all but rule out any further extension of the deadline.
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