In Paris, Secretary of State John F. Kerry says the United States and France agree that the nuclear deal with Iran needs to be stronger. (Reuters)

Secretary of State John F. Kerry wound up a week-long focus on the Iran nuclear talks Saturday by stopping in Paris to consult with European officials on where things stand in the dwindling weeks remaining to negotiate.

“We have made progress,” Kerry said after emerging from talks with French Foreign Minister Laurent Fabius at the Quai d’Orsay. “But there are gaps. We need to close those gaps. We have a critical couple of weeks ahead of us. We are all mindful the days are ticking by.”

Asserting that the United States and its five negotiating partners are holding out for the “right deal,” he added, “And it is frankly up to Iran . . . that asserts it has a peaceful program, to show the world it means what it says.”

Kerry and his Iranian counterpart, Foreign Minister Mohammad Javad Zarif, met over three days in Geneva this past week, and their next meeting is scheduled for March 15, also probably in Geneva.

[Read: Iran nuclear talks going down to the wire]

Graphic: Iran's potential nuclear capability

Kerry stopped in Paris to brief the European nations that are, along with China and Russia, negotiating alongside the United States for a deal to constrict Iran’s nuclear program and introduce a rigorous regimen of inspections to ensure Iran does not cheat. Eventually, there would be sanctions relief for Iran, which is experiencing high unemployment and inflation.

Kerry and Fabius talked alone, then met together with British Foreign Secretary Philip Hammond, German Foreign Minister Frank-Walter Steinmeier and the European Union’s foreign policy chief, Federica Mogherini.

The negotiators are acutely aware that time is running out, as more than a year of intense talks race toward a finish line of their own making. They have given themselves until March 31 to agree on the principles of a deal. Technical details could take an additional three months to iron out.

Now, as the time for talking is being measured in weeks instead of months, officials are at turns optimistic and skeptical about the likely outcome.

Fabius has expressed unhappiness with the concessions Iran has made so far and suggested that a deal with the Islamic republic still faces high hurdles.

He told reporters Saturday that divisions remain on issues of numbers, controls and the duration of any accord. Fabius switched briefly from French to English to quote Iranian President Hassan Rouhani just before an interim agreement was signed in November 2013: “Under no circumstances, we will never seek nor possess any nuclear weapon.”

The world expects no less now, Fabius said.

Concerns have been raised in Europe and in Israel about the possibility of allowing Iran to legitimately operate thousands of centrifuges to enrich uranium to a point where it could amass enough material to make a bomb. Iran has insisted it wants to use enriched uranium only for medical tests, energy and other peaceful purposes.

Others have offered fairly upbeat assessments on the status of the talks. After negotiations with Kerry last week, Zarif put the odds of a deal at more than 50 percent, while Mogherini said Friday that “a good deal is at hand.”

Iran’s nuclear chief, Ali Akbar Salehi, suggested that the latest talks in Switzerland had broken an impasse over technical issues involving a heavy-water reactor at Arak and a uranium enrichment plant at Fordow.

“On enrichment and Arak, we have made very good progress,” he said on Iranian television, though without providing any details. “We have replied to their concerns . . . by making technical proposals while also defending our national interests and our nuclear industry.”