Secretary of State John F. Kerry, left, talks with Iranian Foreign Minister Mohammad Javad Zarif in Geneva. (Susan Walsh/AP)

Significant differences remain between the United States and Iran over a nuclear deal, but the two sides are clear on what needs to be resolved and the urgency of doing it before a June 30 deadline, a senior Obama administration official said Saturday after six hours of talks here between Secretary of State John F. Kerry and Iranian Foreign Minister Mohammad Javad Zarif.

The discussions, the official said, were “intense at times” as both sought clarification of the two biggest issues between them. Iran wants to know exactly which sanctions against it will be lifted and when.

The United States and its global partners in the negotiations want specific mention in a final deal of international verification and monitoring provisions that include all Iranian sites, including military facilities.

Other issues that remain unresolved include the extent to which Iran will provide details of its nuclear research history.

“All issues were reviewed,” but “differences still remain,” Iranian negotiator Abbas Araghchi told reporters as his delegation departed for Tehran.

Asked before the first of two sessions between Kerry and Zarif Saturday whether the deadline for a final agreement will be met, Zarif said, “We will try.”

Much of the talks centered on technical issues that will be part of several annexes to the final accord, which is in draft form. Kerry was accompanied by Energy Secretary Ernest Moniz. Ali Akbar Salehi, head of Iran’s Atomic Energy Commission, joined the talks by telephone from Tehran, where he is recovering from an illness.

Talks between technical experts are due to continue Thursday in Vienna.

Kerry’s schedule has been cleared for all of June, assuming he will have to return as the talks intensify during what is now a 30-day countdown.

The Geneva meeting with Zarif was set up because technical talks that started up several weeks ago, following the April 2 signing of a framework for the final agreement had “gone about as far as they can go” without political decisions from the governments involved, said a senior State Department official traveling with Kerry.

Despite rumblings on both sides about extending the deadline — something that has happened on virtually every previous step in the negotiations during the past year and a half — the United States has said it does not envision an extension. Senior U.S. officials said they remain confident that the deal can be completed on time, assuming political will on both sides.

One possibility for a brief extension, however, may come at the end of the month, when Congress will be in recess through the July 4 holiday. Under the recently passed legislation, lawmakers have 30 days — during which President Obama cannot alter legislatively imposed sanctions — to review the deal, provided it is submitted by July 10.

If it is submitted after that, lawmakers have an additional 30 days for review.

U.S. partners in the negotiations include France, Britain, Germany, Russia and China. The European Union is also at the table.

France has taken a particularly tough stance on the inspections issue. Foreign Minister Laurent Fabius said this week that his government would not sign a final accord unless Iran agrees to open all sites, including military facilities, to verification inspections. Kerry is set to meet with Fabius in Paris next week.

Fabius’s remarks came as Iran’s supreme leader, Ayatollah Ali Khamenei, said he had instructed his country’s negotiating team not to accept military site inspections. Khamenei also said he would “not allow foreigners” to talk to Iran’s nuclear scientists.

Iranian President Hassan Rouhani followed up, saying that “we will never sign a deal that would allow anybody to have access to the country’s scientific and military secrets.”

U.S. officials, as they have in response to similarly tough public pronouncements by Iran in the past, dismissed Khamenei’s remarks.

“What we’re focused on isn’t sort of the rhetoric used at home, but what is agreed inside the negotiating room,” said the official, who spoke on the condition of anonymity under ground rules set by the State Department.

Read more:

How to win the Iran argument

Verdicts often set before trials take place in Iran’s revolutionary courts

Kerry attends inauguration of Nigeria’s new president

Today's coverage from Post correspondents around the world