Meeting in Vienna in a final round of talks between Iran and six world powers before Monday's deadline to agree a deal, the differences are few in number but of major significance.
Speaking in Paris on Thursday before flying to Vienna, Kerry said, however, that the possibility of putting more time on the clock -- as happened in July with an earlier deadline -- was not on the table.
"We are not discussing an extension. We are negotiating to have an agreement. It's that simple," Kerry said.
He added however that the United States and all the other powers were "concerned about the gaps".
Britain's Foreign Secretary Philip Hammond had said on Wednesday that he was "not optimistic" the deadline could be met, suggesting that the best hope was for another extension.
"I think if we make some significant movement, we may be able to find a way of extending the deadline to allow us to get to the final deal," Hammond said in Riga.
Russia's main negotiator in the talks, Sergei Ryabkov, said Thursday that the talks were being held in a "tense atmosphere" and that agreeing the mammoth accord would be tough.
"In the current situation it will be very difficult to get a deal unless there is a new spirit," Ryabkov was quoted as saying by Russian agency RIA Novosti.
Iran's speaker of parliament Ali Larijani meanwhile told Iranian media: "We are constantly cooperating (but the other side) is raising the tone."
He added: "We hope that the other side will behave in a rational manner... and won't take the wrong path."
French Foreign Minister Laurent Fabius, who together with Hammond was expected in Vienna on Friday, said there remained "major differences".
"We hope that they can be bridged but that depends to a very large extent on Iran's attitude," Fabius said at a joint news conference with Kerry in Paris.
Iran's Foreign Minister Mohammad Javad Zarif believes however that the onus is on the other side, urging them not to make "excessive demands".
Twelve years
Iran and the six powers -- the US, China, Russia, Britain, France plus Germany -- have been negotiating intensively since February to turn an interim accord with Iran reached a year ago into a lasting agreement before November 24.
Such a deal, after 12 years of rising tensions, is aimed at easing fears that Tehran will develop nuclear weapons under the guise of its civilian activities -- an ambition the Islamic republic has always hotly denied.
Some areas appear provisionally settled in what would be a highly complex deal that would run for many years, even decades.
But two key issues remain: enrichment -- rendering uranium suitable for peaceful uses but also, at high purities, for a weapon -- and the pace of the lifting of sanctions.
Diplomats say Iran wants all sanctions lifted at once. The six world powers want however to stagger any suspension to be sure that Iran would not renege on its commitments.
Iran wants to massively ramp up the number of enrichment centrifuges -- in order, it says, to make fuel for a fleet of future reactors -- while the West wants them dramatically reduced.
Iran's nuclear chief Ali Akbar Salehi stuck to this position on Thursday, saying Iran would increase its enrichment capacity to around 20 times its current ability within eight years.
"A deal is still possible by November 24," Arms Control Association analyst Kelsey Davenport told AFP.
"The remaining obstacles can be overcome if both sides are willing to show some flexibility."
