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But Mr. Obama also made clear that the longer Mr. Gbagbo holds on, and the more complicit he becomes in violence across the country, the more limited his options become, said a senior administration official. The official insisted on anonymity to speak about administration strategy.

Mr. Rhodes said the White House understands that U.S. involvement in African politics can be viewed as meddling. But he said Mr. Obama can speak to African leaders with a unique level of candor, reflecting his personal connection to Africa — his father and other family members have been affected by the corruption that plagues many countries there.

Officials also see increased political stability in Africa as good for long-term U.S. interests — a way to stem the growth of terrorism in east Africa and counterbalance China’s growing presence on the continent.

The United States was caught off guard during the 2009 climate summit in Copenhagen when several African countries voted with China and not the United States, an administration official said. The official said the administration must persuade African nations that their interests are better served by aligning with the United States.