THE stunning election of a pragmatic former Iranian nuclear negotiator, Hassan Rowhani, has offered the Obama administration a once-in-a-lifetime chance to end the atomic stalemate with Iran.

In the West, Mr. Rowhani is widely seen as a turbaned politico from inside the establishment. One of us has worked for him directly, as his deputy in nuclear talks. The other has conducted research at the think tank he runs. We can attest that he is wary of a purely ideological approach to foreign policy and is driven by more than simple expediency in pursuit of the national interest. After seeing the nuclear deal he was attempting to negotiate with the European Union fall apart in 2005, Mr. Rowhani is now seeking to resolve the nuclear issue once and for all, and also to redeem himself politically.

Mr. Rowhani’s victory demonstrates that there is now real momentum toward the initiation of direct talks between Iran and the United States. Despite remarks he has made to appease hard-liners since his victory, Mr. Rowhani’s campaign rhetoric made clear his desire to change the hostile relationship with America. In recent months, even Iran’s supreme leader, Ayatollah Ali Khamenei, has given permission for direct negotiation — although he has not expressed optimism about its prospects.

The single biggest threat to this unique window for dialogue is misguided perceptions of each side’s respective strengths and weaknesses. To avoid squandering this opportunity, President Obama and President-elect Rowhani, who takes office in August, must resist and debunk the false impressions that have been promoted by extremists on both sides.