Ban said through his representative that Washington's leadership at the United Nations was "essential" considering the complex challenges before the world community.
Rice in a speech Wednesday at New York University said, "The United Nations is imperfect, but it is also indispensable. There can be no substitute for the legitimacy the United Nations can impart or its potential to mobilize the widest possible coalitions."
She noted the world body was "essential" to efforts to establish a coalition to ensure U.S. national interests were secured.
Ban in his statements welcomed the opportunity to work with a diplomatically engaged U.S. government.
"The secretary-general is committed to continuing the reform process and looks forward to working with the United States," it read.
Washington's ties to the United Nations soured somewhat when U.S. President George W. Bush installed John Bolton as the U.S. envoy.
Bolton in the 1990s had said several floors of the U.N. headquarters in New York City could be removed and nobody would notice.