Speculation about possible talks between Obama and Rouhani in particular has been mounting because the counterparts spoke by phone last year on the sidelines of the annual United Nations General Assembly.
"I don't know that either of those individuals will appear on the president's dance card next week," Earnest said when asked about potential meetings involving Obama and Putin or Rouhani.
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The Obama-Rouhani call last September marked an historic high point in the effort to defuse tensions between Tehran and Washington, as part of talks that led to an interim deal on Iran's nuclear program and talks on a permanent pact.
Political sensitivities, as nuclear negotiations reach a critical stage, and the US intervention in Iran's neighborhood against Islamic State militants in Iraq and in future in Syria, may augur against any direct contact between Obama and Rouhani at the UN this time around.
Supreme leader Ali Khamenei exacerbated the back-and-forth between Washington and Tehran by saying earlier today that Iran had rejected a US request for cooperation over the IS crisis.
In response, the White House said it did not coordinate military or intelligence operations with Iran -- with which it has been locked in a virtual Cold War for over 30 years -- but did not rule out "back channel" conversations on issues including the nuclear negotiations.
Putin and Obama last met informally on the sidelines at a lunch for world leaders at the 70th anniversary commemorations of the D-Day landings in Normandy, France, in June.
Since then, Washington has imposed several rounds of sanctions on Moscow to punish what it sees is its "brazen" military interference in Ukraine.
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