(Jewel Samad/)

Following a week of speculation and rising expectations, White House officials today seemed to downplay the prospect of a one-on-one meeting between President Obama and his Iranian counterpart.

"We are hoping to engage with the Iranian government at a variety of levels, provided they will follow through on their commitment to address the international community's concerns over their nuclear program," Deputy National Security Adviser Ben Rhodes told reporters on Air Force One.

The caveat regarding its nuclear program is a new twist in the administration's rhetoric after days of suggesting openness to meet without hinting at a prerequisite.

The White House has not ruled out a less formal encounter between Obama and Rouhani, including a handshake, on the sidelines of the U.N. General Assembly during the day on Tuesday. The most likely opportunity for such a greeting would be a midday luncheon hosted by Secretary General Ban Ki-moon.

"I don't think anything will happen by happenstance on a relationship on an issue that is this important," Rhodes said. No American president has met one-on-one with an Iranian head of state since 1977."

Meanwhile, the administration quietly announced that Secretary of State John Kerry will meet with Iran's Foreign Minister Javad Zarif in New York - a meeting that would be the highest-level contact between the two governments on the nuclear issue.

The State Department said the meeting will take place Thursday afternoon as part of a larger group - the so-called P5+1 - seeking to reach an agreement over Iran's contested nuclear program.

"This opportunity with the Iranian foreign minister will give our (P5+1) ministers a sense of their level of seriousness and whether they are coming with concrete new proposals and whether this charm offensive actually has substance to it," one senior State Department official said of the meeting.

"No one should go into Thursday with the expectation that we're going to resolve the decades long discussion over their nuclear program," another official said.

This post has been updated.