WASHINGTON — Secretary of State Hillary Rodham Clinton said Tuesday that Iran had a “clear opportunity” to engage with the international community, amplifying the conciliatory tone struck a day earlier by President Obama toward Iran and the rest of the Muslim world.

Sketching out an ambitious diplomatic agenda, Mrs. Clinton also suggested that there could be some form of direct communication between the United States and North Korea. And she said relations with China had been excessively influenced by economic issues during the Bush administration.

Mrs. Clinton, in her first remarks to reporters since becoming the nation’s chief diplomat, said, “There is a clear opportunity for the Iranians, as the president expressed in his interview, to demonstrate some willingness to engage meaningfully with the international community.”