Whoever is crafting the messages for Iran’s leaders these days is doing a smashing job making it appear as if the Islamic republic has taken a dramatic turn toward engagement and moderation. Regardless of whether Iran’s conciliatory Twitter feed and Facebook diplomacy is genuine, it deserves a serious response from the U.S. and its allies.

The director of Iran’s Atomic Energy Organization has said Iran is very optimistic about breakthroughs in nuclear negotiations in coming months. President Hassan Rohani has exchanged letters with his U.S. counterpart, which he says could be the beginning of something good. Even the normally gruff supreme leader, Ayatollah Ali Khamenei, is sounding conciliatory, saying Iran should pursue “heroic leniency” to resolve the diplomatic conflict over its nuclear program.

The question, of course, is whether this is for real or whether Iran is playing for time -- and its interlocutors for fools. Iran is thought to be less than a year from having the ability to process low-enriched uranium into sufficient material for a nuclear bomb without being detected by international inspectors. The Iranians could be putting up a front to extend negotiations through that period and forestall a military strike on its nuclear facilities by the U.S. or Israel.

Or, the campaign could be intended to serve its stated purpose: to resolve Iran’s confrontation with the world’s major powers over its nuclear program, ease sanctions and thus enable the country to rebuild its economy. Rohani himself has identified this agenda as his top priority.

Iran’s inner workings are too obscure for anyone to say with confidence which explanation is correct. Nevertheless, there are good reasons to lean toward the latter. Rohani and those around him are pragmatists above all. They understand that Iran can’t prosper unless it re-enters the global financial system and is allowed to resume significant oil exports.

At the time of Rohani’s election, there were doubts that he would have the mandate to determine nuclear policy, but he told Ann Curry of NBC News that he had “full power and complete authority” to make a nuclear deal. An Iranian president isn’t likely to make such a comment offhandedly, for fear of setting off the temperamental Khamenei.

If Iran’s leaders are only faking their moderation, they’ll have a lot of explaining to do at home when the masks come off. In repeatedly stressing that they wish to distinguish themselves from the provocative government of former President Mahmoud Ahmadinejad, that they have no intention to build a nuclear bomb, and that they seek engagement with the U.S. and other powers, Iran’s leaders are building a constituency for those positions within Iran -- and they know it. That’s another reason to think they may be sincere.

In determining how to respond, the U.S., fortunately, doesn’t have to know Iran’s intentions. It only has to know its own: to prevent Iran from acquiring a nuclear weapon, ideally without resorting to force.

The broad outlines of a deal accomplishing that are fairly well understood. The five members of the United Nations Security Council plus Germany would acknowledge Iran’s right to enrich uranium and would lift sanctions. Iran would agree to forgo enrichment to 20 percent and would honor its full obligations to the International Atomic Energy Agency. Those include inspections of all known nuclear facilities, which would give the world a window on the Iranian program that would make the intentions-guessing game far less relevant.

Sequencing has been a problem. The U.S. has been loath to clearly recognize what Iran calls its “right to enrich,” and the world powers have offered only piddling sanctions relief. Iran’s PR campaign appears to be aimed at breaking that impasse.

The least the U.S. and its partners can do is respond by emphasizing that Iran would be able to enrich uranium, to a limited extent, in any deal and by setting out a clear schedule for lifting sanctions. This may be what the Iranians need to give up the nuclear ambiguity they now maintain: a reasonable assurance that they won’t be punished forever, no matter what they do.

Whether President Barack Obama meets with Rohani at next week’s UN General Assembly -- the White House hasn’t ruled out the possibility -- or the U.S. engages Iran in some other fashion, Iran’s recent overtures are too intriguing to ignore.

To contact the Bloomberg View editorial board: view@bloomberg.net.