Obama 'open to engagement' with Iranian president at United Nations meeting

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Rhodes did insist that any meeting would be conditioned on Iran following "through on their commitments to address the international community's concerns over their nuclear program."

But despite no scheduled meeting between the world leaders, Rhodes dismissed the likelihood that a handshake meeting between Obama and Rouhani would occur by happenstance.

"I don't think that anything would happen by happenstance on a relationship and an issue that is this important," Rhodes said. "So I think, clearly, this is an issue that we devoted as much time to as any other issue on our national security agenda for the last five years. We have had a very carefully structured policy both in terms of the sanctions that we put in place on Iran and in terms of how we engage with the Iranian government and the international community on this issue."

In recent weeks, Rouhani has said that he is eager to negotiate an end to financial sanctions placed on his country because of its nuclear program. He has also insisted Iran has no interest in pursuing nuclear weapons.

On Capitol Hill, influential lawmakers including Sens. Robert MenendezRobert (Bob) MenendezIn judge's 2010 Senate trial, Menendez was guilty of hypocrisy Excused Menendez juror: 'I don't think he did anything wrong' We don't need a terrorist attack to know diversity program has to go MORE (D-N.J.) and Lindsey GrahamLindsey Olin GrahamCNN to air sexual harassment Town Hall featuring Gretchen Carlson, Anita Hill Trump wrestles with handling American enemy combatants Flake: Trump's call for DOJ to probe Democrats 'not normal' MORE (R-S.C.) warned the president not to decrease sanctions “unless accompanied by real, meaningful action by the Iranian regime."

"Like you, we viewed the election of Hassan Rouhani as an indicator of discontent amongst the Iranian people and we have taken note of recent diplomatic overtures by Iran," they wrote. "However, whatever nice words we may hear from Mr. Rouhani, it is Iranian action that matters."