Even so, they said they wanted to test Mr. Rowhani quickly, noting that although he argued for a moderate tone in dealing with the United States and its allies when he was a negotiator, he also boasted in 2006 that Iran had used a previous suspension of nuclear enrichment to make major strides in building its nuclear infrastructure.

On the CBS program “Face the Nation” on Sunday, Denis McDonough, Mr. Obama’s chief of staff, said of Mr. Rowhani’s election over the weekend: “I see it as a potentially hopeful sign. I think the question for us now is: If he is interested in, as he has said in his campaign events, mending his relations — Iran’s relations with the rest of the world — there’s an opportunity to do that.” But Mr. McDonough said doing so would require Iran “to come clean on this illicit nuclear program.”

Another senior administration official, speaking on the condition of anonymity, noted that for Mr. Rowhani, “wanting to end Iran’s isolation is different from agreeing to move the nuclear program to a place where it would take them years to build a weapon.”…

Mr. Rowhani gave a glimpse of his views on negotiating strategy in a speech in 2004, which leaked out of Iran two years later. “While we were talking with the Europeans in Tehran,” he recalled at the time, “we were installing equipment in parts of the facility in Isfahan,” a major production site. “By creating a calm environment, we were able to complete the work in Isfahan.”