Saturday’s exchange was a key moment for President Obama—now he will have to contend with how it the America public will react. (Zoeann Murphy/The Washington Post)

Washington Post correspondent Jason Rezaian and two other Americans released from an Iranian prison landed Sunday at Ramstein Air Base in Germany and were expected to be whisked immediately to the nearby U.S. military medical center at Landstuhl.

Rezaian is accompanied by his mother and his wife, Yeganeh Salehi, an Iranian who was allowed to leave the country with him. His brother, Ali Rezaian, and senior Post editors awaited his arrival in Germany.

Executive editor Martin Baron said they had no information on when they would be allowed to see Rezaian. His family has said his health seriously deteriorated during his 18-month detention.

“We’ll play it day by day, and make sure that whatever happens is what’s best for Jason, and what he wishes,” said Post Foreign Editor Douglas Jehl. “We’re eager to welcome him back to the Post family.”

In a statement Sunday morning, President Obama said that all five Americans released had been “unjustly detained,” and in some cases faced long prison sentences in Iran. Those traveling with Rezaian included Saeed Abedini, an Idaho cleric, and former U.S. Marine Amir Hekmati. All are U.S.-Iranian dual nationals. Little is known about a fourth released prisoner, Nosratollah Khosravi-Roodsari, who the administration said opted not to join the flight. A fifth American, student Matthew Trevithick, was separately released and left Iran on his own.

Although the prisoners were released Saturday, the Swiss Air plane that was there to take them out of Iran was delayed many hours before takeoff. Administration officials said Obama waited to speak only after their departure was confirmed.

Secretary of State John F. Kerry said the delay was due to last-minute misunderstandings over whether Rezaian’s mother, Mary Rezaian, and his wife were on the flight manifest. The departure was also complicated by flight crew rest rules, he said.

Mary Rezaian, who was in Iran while her son was put on trial on espionage and related charges, was not officially part of the agreement; she was placed on the plane manifest at the request of the Americans. Both she and Salehi were initially prohibited from boarding.

Kerry said it required the intervention of Iranian Foreign Minister Mohammad Javad Zarif, who dispatched four aides to work through the “glitch” so the plane could leave as part of a carefully choreographed deal in which Obama offered clemency to seven Iranians.

“Zarif had no question about it,” said Kerry during a 3:30 a.m. interview with four reporters traveling with him from Vienna, after the plane landed at Joint Base Andrews in Maryland. “It was part of the agreement; it was clearly stated. The problem was, one of the guys on the ground, at a military base, didn’t have it on the manifest."

Kerry said he told Zarif: “Javad, look, it’s part of the agreement. She’s on the list."

“He assigned four people to it immediately. Before I left and got on the plane, we had complete clarity. . . . She was going to go. It was just a glitch.”

“I hope America wakes up to the news they are in the air and on their way,” Kerry said. The plane eventually departed at about 7 a.m., Washington time.

Kerry said plans called for the freed Americans to be met in Geneva, their first stop, by Patrick Kennedy, the undersecretary of state for management, and Brett McGurk, the assistant secretary of state for Iraq and Iran, who spent 14 months negotiating the prisoner deal.

He said the complex arrangement, which also involved U.S. clemency for seven Iranians charged or convicted for violations of sanctions against Iran, was hammered out in a dozen meetings he held with Zarif in the months after a nuclear deal negotiated between world powers and Iran was finalized in July. The deal was formally implemented Saturday.

Though Kerry and Zarif had discussed the imprisoned Americans on the sidelines of every nuclear negotiating session, he said, the focus turned exclusively to the prisoners during talks after the nuclear agreement was concluded. During their first face-to-face encounter after that landmark agreement, at a multi-national meeting in Vienna in November to discuss possible Syrian peace talks, Kerry believed they had resolved the prisoner issue as well.

“We actually shook hands thinking we had an agreement,” he said. “I thought it was done."

But that was apparently blocked, Kerry said, by "some folks back in Tehran in a different department. I don’t want identify it; I don’t want to embarrass people and cause problems. It was just one of those natural interagency, any government, differences. . . . So we went back to work grinding out that differential.”

Kerry said the negotiations hit a snag over Iranian demands for its citizens held in the United States. Iranian officials initially said they wanted freedom for 19 prisoners, a number that eventually was whittled to seven, all but one of them holding dual U.S.-Iranian citizenship.

“Iran asked for a lot of people,” Kerry said. “We said no. We said no, we said no, we said no to specific people they wanted until it became clear we were not going to let out hardened criminals, somebody accused of murder, of narcotics.”

Kerry said Obama insisted that the only Iranians the United States would consider releasing were those convicted or charged with violating nuclear-related sanctions that were lifted Sunday as the nuclear agreement was implemented.

“There was a symmetry here,” Kerry said.

Not all the seven Iranian prisoners will return to Iran, Kerry said. That was determined by U.S. consular officials who visited them in person to ask their preferences, a task that was mirrored in Iran with visits to the American prisoners by consular officials from the Swiss Embassy that represents U.S. interests in Iran.

Kerry said a written agreement ensures Iran will cooperate with U.S. officials investigating the whereabouts of Robert Levinson, a former FBI agent who disappeared in Iran in 2007. Kerry said he has “no idea” if Levinson is alive or dead. Kerry said he spoke recently with Levinson’s wife, assuring her the United States will continue to search for him, and Iran has agreed to cooperate in that search..

“We are making our very best effort, taking the last information known regarding his whereabouts,” Kerry said. “He was absolutely part of every discussion.”

Kerry said the United States also would continue negotiating with Iran over the release of Siamak Namazi, a Dubai-based U.S. citizen who was detained last fall. He is not part of the written agreement, however.

Kerry said he had been confident the negotiations would succeed eventually.

“I always believed we’d get there sometime,” he said. “But I couldn’t tell whether it was going to get super complicated by the insertion of this other agency and political dynamics into the mix. . . . But in the end, [Iran] worked hard and did the things yesterday they said they would do, and we did things.”

Kerry said that he hopes that negotiations for the prisoner deal herald a new day when Iran and the United States can iron out their differences at the negotiating table, but he said there are no guarantees.

“There are no other deals, no side deal to this,” he said. “Nothing is hidden here. What you see is what you get. People are out and free. We still have problems with Iran. None of this wipes away our concerns with Iran. We have to continue to work at those. But you have to start somewhere. And this is a beginning.”