Speaking just before huddling again with Iranian Foreign Minister Mohammad Javad Zarif, Kerry said Washington still believed an accord was possible by a November deadline.
"It remains our fervent hope that Iran and the P5+1 can in the next weeks come to an agreement that would benefit the world," the US secretary of state told a meeting at the UN on the Comprehensive Nuclear Test Ban Treaty (CTBT).
Dismissing skepticism about the twists and turns of the complex negotiations led by a group of nations known as the P5+1, Kerry said the talks had already borne fruit.
"The interim agreement that we struck with Iran... has made the world safer because a nuclear stockpile that was at 20 percent has been reduced," Kerry said.
But Iranian President Hassan Rouhani, who is impatient to see crippling economic sanctions against his country lifted, said the pace of the negotiations had to be picked up.
"The remaining time for reaching an agreement is extremely short. Progress that has been witnessed in the last few days has been extremely slow," Rouhani told reporters at the UN.
After a bid to reach a comprehensive deal to rein in Iran's suspect nuclear program by July failed, the negotiators set a new deadline of November 24.
Rouhani said Iran had shown flexibility and now "the ball is in the interlocutor's court."
"The progress realized so far has not been significant," he said. "We must strive forward and take more significant steps."
But US officials have said they are awaiting more moves from Iran.
One of the thorniest issues is the question of enrichment.
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The West wants Iran to dismantle virtually all but a few thousand of its 19,000 centrifuges which can be used to develop weapons-grade uranium.
But Iran bristles at destroying machines in which it has invested billions of dollars, and says it should retain the right to enrich for its civilian nuclear energy program.
"At this time as I speak, there is no significant progress," French Foreign Minister Laurent Fabius said earlier Friday.
Russian Foreign Minister Sergei Lavrov said he remained "cautiously optimistic" amid the negotiations being led by Britain, China, France, Russia, the United States plus Germany.
"We still have time," he told reporters. "We will do our utmost to make sure that remaining small, but extremely important, issues be resolved in a way that is acceptable to all."
A Western diplomat said a lot of technical work had been done during the past week, urging all sides not to get hung up on numbers of centrifuges.
"Numbers shouldn't be an obsession. We can be creative, but at the end of the day we need serious commitments from Iran on precise facts, technical points," the diplomat said.
But he acknowledged "we are still expecting significant moves from the Iranian side," adding the level of "mistrust is pretty high."
Under the 2013 interim deal, Iran agreed to freeze parts of its nuclear program and allow daily inspections of some nuclear sites in return for a partial release of billions of dollars from blocked oil revenues.
The final deal would aim to ease fears Iran is seeking to develop an atomic bomb, by expanding the time needed for Tehran to make such a weapon and allowing for a tough monitoring regime by the UN nuclear watchdog, the IAEA.
"The objective is really to have Iran reduce significantly its enrichment capacity," the Western diplomat said.
"In return the six are ready to lift sanctions step by step, starting with the EU sanctions and the US unilateral sanctions. That's a huge reward for the Iranians."