First there was a handshake, then an invitation to talk and finally a 30-minute tete-a-tete that made for the highest-level official meeting between the United States and Iran in more than three decades.

The opportunity for a rare meeting between US Secretary of State John Kerry and his Iranian counterpart, Mohammad Javad Zarif, came after talks concluded between Zarif and foreign ministers from the six major powers on resolving Tehran's disputed nuclear program.

At the start of the talks, Kerry and Zarif shook hands, a senior U.S. official told reporters.

Zarif and Kerry were then seated side by side at the corner of a U-shaped table during the meeting of foreign ministers from the five permanent members of the UN Security Council - Britain, France, Russia, China, the United States - and Germany, known as the P5+1.

At the end of the meeting, Kerry seized the opportunity to invite Zarif for private talks, according to the senior U.S. official, speaking on condition of anonymity.

"The secretary leaned over and said, 'Shall we talk for a few moments?'" the official said.

The two diplomats went into a room to the side of the main meeting hall where they met one-on-one without their aides, according to the official. "Informally there had been some chatting it might happen," the official said.

That 30-minute session was the highest-level official meeting between the United States and Iran since the 1979 Islamic Revolution and the taking of American hostages at the U.S. Embassy in Tehran that ushered in a more than three-decade estrangement between the two nations.

Earlier in the week, there had been speculation about a possible encounter between U.S. President Barack Obama and Iranian President Hassan Rouhani during the U.N. meetings, which would have been symbolically important given the strains between Washington and Tehran.

While the White House was open to a meeting between Obama and Rouhani in New York, the Iranians indicated it was too complicated, an Obama administration official said.