The Iran nuclear talks will spill beyond a Tuesday deadline, officials said Sunday as Iran’s foreign minister broke off from the negotiations and flew to Tehran for consultations.

A potential agreement to rein in Iran’s nuclear program in exchange for sanctions relief remains elusive in this final round of talks, the culmination of more than 19 months of intense negotiations. Major differences still divide the two sides: Iran on the one hand and six world powers, including the United States, on the other. The key unresolved issues concern the pace at which sanctions would be lifted and how much access Iran would grant international inspectors who would monitor its compliance.

In a sign that negotiations have deteriorated since a framework agreement was reached April 2 in Lausanne, Switzerland, British Foreign Secretary Philip Hammond told reporters that the participants are squaring off over “differences of interpretation” in the deal’s contours that were supposedly settled in Switzerland.

“There is going to have to be some give or take if we are to get this done in the next few days,” he said.

Iranian Foreign Minister Mohammad Javad Zarif met for about 20 minutes with Secretary of State John F. Kerry before flying back to Tehran on Sunday. His absence until Tuesday was considered a sign that he needs more instructions from Iran’s leaders on offers put before him by the five permanent members of the Security Council plus Germany.

U.S. negotiators appeared unruffled by Zarif’s departure and suggested his trip home could help break a logjam.

“If people need to go back to their capitals for conversations with their leaderships, that’s a good thing,” said a senior State Department official, speaking on the condition of anonymity to comment on the secret talks.

But the official acknowledged it will be all but impossible to reach a comprehensive agreement before the June 30 deadline and said the talks would continue for “a few days” beyond it.

Since Lausanne, the Iranians have publicly backed away from some of the agreements reached there. Supreme Leader Ayatollah Ali Khamenei last week listed seven “major red lines” Iran would not sign on to for a final deal. They included a demand that all financial and economic sanctions be lifted the day a deal is reached, a prohibition on letting the International Atomic Energy Agency inspect military sites and a rejection of a long-term deal of 10 years or more.

It is not known, however, whether Khamenei was staking out a hard negotiating position for the final phase or whether his red lines are firm enough to scuttle a deal.

Underscoring what could happen if the talks fail, a senior Iranian official warned that Tehran could resume enriching uranium at a faster pace after putting much of it on hold while the talks were underway.

“Do not think that Iran needs a deal,” said Ali Larijani, speaker of the Iranian parliament, according to a report Sunday on the Islamic Republic of Iran Broadcast. “We welcome an agreement, but I do not [want] you to think that if you exert more pressure, Iran will tolerate it. Do not make Iran withdraw from the talks, and do not make it follow its nuclear path more speedily.”

Federica Mogherini, the European Union’s foreign policy chief, said getting a deal at the 11th hour would be “tough” but not impossible.

“It’s a matter of political will,” she told reporters.

Not all the drama was inside the hotel where the talks are being held.

Relatives of Amir Hekmati, a former Marine arrested in 2011 on a visit to see his grandmother and sentenced to 10 years for “cooperating with hostile governments,” came to Vienna to plead for his release during the Ramadan holiday. Hekmati will pass his 1,400th day in Iranian custody Monday.

“Ramadan is a time of mercy and compassion,” said Sarah Hekmati, his sister, who is asking the Iranian government to allow her brother to come home before their father dies of terminal cancer. “We are here to make sure Amir is not forgotten. We want his case to not be an afterthought.”

Hekmati said she had tried to press her brother’s case directly with Iranian diplomats. But she said she had been rebuffed by the Iranian Embassy in Vienna, and also in London, where the talk-show host and veterans’ advocate Montel Williams delivered a letter on her behalf. She approached Iranian reporters covering the talks, but she said they sidled away from her nervously.

Hekmati said she hoped the nuclear talks would give the family some leverage in agitating for her brother’s freedom, because his release might remove one objection Congress has to approving a deal with Iran.

In sideline talks with Iran, State Department negotiators have repeatedly raised the case of Hekmati, as well as those of imprisoned pastor Saeed Abedini and Washington Post reporter Jason Rezaian, and the disappearance of former FBI agent Robert Levinson. While Hekmati said she appreciated the effort, it has been futile.

“They’ve done more for other people,” said her husband, Ramy Kurdi, citing Bowe Bergdahl, the soldier who was swapped for five Taliban prisoners, and Alan Gross, released from a Cuban jail when Washington decided to normalize relations with Havana. “He’s not home. And they are.”

Also in Vienna was Ali Rezaian, whose brother, Jason, was arrested more than 11 months ago. He is standing trial on a charge of espionage and other related charges, an allegation vigorously disputed by the State Department and The Washington Post.

Ali Rezaian said he stopped in Vienna after visiting his mother, Mary Rezaian, in Istanbul. She recently left Tehran after being prohibited from attending her son’s trial but plans to return when the trial resumes.

“Jason asked her to come back,” he said of phone calls Mary Rezaian had with her son while in Tehran. “It’s more than frustrating. It’s inhuman. It’s heartbreaking. They told her to come back for the trial, and 24 hours before it began, they said she couldn’t attend.”

Rezaian said his brother’s attorney told them the trial is unlikely to resume until after Ramadan ends in mid-July.

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