"We have difficult issues to resolve," Kerry told reporters in Vienna.
He said while negotiators have made progress, there are still major points of contention -- and that foreign ministers involved in the talks will arrive Sunday evening in hopes of finalizing the deal.
"At this point negotiations could go either way," he said. "If hard choices get made in the next couple of days and made quickly we could get an agreement this week. But if they are not made, we will not."
Iranian Foreign Minister Mohammad Javad Zarif said Friday in a video message that the countries had "never been closer" to a deal.
That video inflamed tensions in the United States, where Republicans are skeptical about the negotiations' outcome.
Sen. Tom Cotton of Arkansas, who has led the GOP's resistance to the deal, said Zarif's video, "with his smug, condescending tone, shows just how far down the path we've gone toward Iran's position."
"Iran should have faced a simple choice: They dismantle their nuclear program entirely, or they face economic devastation and military destruction of their nuclear facilities," Cotton said. "As that video shows, they think they're negotiating from a position of strength and that they hold all the cards."
Experts from the countries involved in the Iran nuclear negotiations have reached a tentative agreement on language dealing with sanctions relief, a source familiar with the talks told CNN on Saturday.
It is the first noticeable sign of progress in these discussions, which have been slow-going. However, the source said there is a lot of work to do and this language still has to be presented to the foreign ministers of the countries involved in the talks, meaning this is far from complete.
"We have resolved many problems so far, but there are still questions to be tackled on nuclear as well as sanctions issues," a senior Iranian diplomat directly involved in the nuclear talks told CNN.
Earlier, a senior administration official told the pool traveling with Kerry that, "Even if and when issues get resolved at an experts level, there will remain some open issues that can only be decided by ministers."
A source directly involved in the talks said the sides would declare at a deal signing that sanctions are lifted, allowing Iran to claim at home that they got immediate relief. But the sanctions would only be lifted over time as Iran meets its various obligations, allowing the West to stick to its commitment to conditional relief.
This would come in addition to certain funds being released right away as part of the so-called "signing bonus," the source added.
Kerry and Iran's Zarif held an impromptu discussion at the Coburg in Vienna on Saturday afternoon, and were scheduled to meet later in the evening, a senior State Department official said.
Officials on both sides of the negotiating table have said they are hopeful they will be able to broker a final deal on Iran's nuclear program but have emphasized in recent days that gaps remain over items that could make or break the deal.
Iran reached a preliminary agreement over its nuclear program in April after multiple rounds of negotiations with the P5+1 countries -- the United States, UK, France, China, Russia and Germany. But negotiators must iron out the details and resolve contentious differences on critical issues, including inspections of nuclear sites.
Iran also needs to resolve outstanding issues with the UN's International Atomic Energy Agency, which is responsible for probing and inspecting Iran's nuclear program. The agency is still trying to get Iran to hand over additional documents and information that would shed light on the past military aspects of Iran's nuclear program, which the country has insisted has always been peaceful.
After meeting with Iranian President Hassan Rouhani on Thursday, IAEA chief Yukiya Amano said that he believes "both sides have a better understanding on some ways forward," but added that "more work will be needed."