President Obama, in asserting that the choice we face with Iran is “between diplomacy and some form of war,” misjudges the Islamic Republic. It is already at war. Nor does Mr. Obama’s agreement actually achieve its stated objective: to prevent, or even meaningfully delay, Iran’s acquisition of nuclear weapons capabilities. Congress is right to challenge the accord.

I can claim some understanding of Iran, if not of the President’s thinking. My family ruled the country as Shahs of the Qajar Dynasty between 1785 and 1925, and again under a democratically-elected prime minister, Mohammad Mossadegh, between 1951 and 1953. I witnessed Ayatollah Khomeini consolidate his power in the summer of 1979.

That was after Khomeini’s overthrow of Mohammad Reza Shah Pahlavi, whose father had been installed with British support and on whose account America and Britain overthrew Mossadegh. Then, it was about control of Iranian oil. And yes, Iran was a victim. Now it’s about worldwide jihad, and Iran is the aggressor.

Iran’s Supreme Leader, Ali Khamenei, and his Revolutionary Guards are driven by a mission imposed on Iran by its constitution. Any deal that ignores this is futile. Khomeini promulgated the Constitution in 1979. It proclaims “the ideological mission of jihad,” which it defines as “extending the sovereignty of God’s law throughout the world,” through Iran’s Army and the Islamic Revolutionary Guards Corps.

To treat with the Islamic Republic over the particulars of its weaponry while failing to address the very purpose of its bellicosity is delusional. The so-called Joint Comprehensive Plan of Action does nothing to change the fact that, in plain Farsi, Iran is committed to world conquest by Islam, with its clerics as warlords. Those to be conquered include America (the “Great Satan”), Israel (the “Little Satan”) and the Sunni-led Gulf States.

Iran’s support for terrorism in the Middle East and elsewhere is evidence enough that the regime takes this mission to heart. The ink on the JCPOA was barely dry when it was reaffirmed by Khamenei. “Even after this deal our policy towards the arrogant U.S. will not change,” he vowed. “We don’t have any negotiations or deal with the U.S. on different issues in the world or the region.” The death chants are led by Iran’s leaders. They are not meaningless theater.

If Iran’s holy war continues (as it does) despite this deal, what is the purpose of lifting sanctions and releasing $150 billion in frozen assets, thereby providing vast resources to finance it? Iran needed an atomic program less to wage its jihad than to manipulate America into lifting sanctions. Which is what Iran accomplished at Vienna, along with gaining such benefits as the lapse in a few years of constraints on arms trafficking and enhanced verification, such as it is, a few years later.

That’s the official timing. The Islamic Republic, though, has demonstrated its skill at circumventing agreements and its willingness to do so. It can reap the benefits early, then cheat when it chooses. If caught, commercial interests will undermine the supposed “snap-back” of sanctions. The regime also understands that if U.S. military action is off the table today, when Iran is weakened, then surely the risk is even lower down the road. The Vienna accord might properly be named the Joint Comprehensive Plan of Inaction.

Yet the pact’s fatal flaw is its failure to address the illogic of any agreement with Iran in the first place: the Islamic Republic’s evangelism by scimitar, a war embedded in its very constitutional raison d’être — and already underway.

Iranians express anxiety over their own defense, surrounded as they are by nuclear powers and challenged by Sunni extremists who would slit their throats as heretics. They and America may share, in ISIS, some common enemies. That does not make Iran an American ally. Even if the Islamist menace were defeated, Iran’s jihad stands so long as it remains enshrined in the Constitution. Iran is threatened largely because it has constitutionally defined itself as a threat.

If this Administration can’t negotiate a deal with Khamenei that incorporates not only real verification and that repeals sanctions only in return for positive changes in behavior — including a constitutional amendment stripping global jihad from its founding revolutionary purpose—then no deal is the best alternative.

Ayatollah Khamenei’s victory in Vienna strengthens regime hardliners, but there are other voices in this nation of 80 million people. Mainstream Shiism does not subscribe to Ayatollah Khomeini’s militant school combining church and state. Many Iranians hunger for freedom, even if President Obama is silent on their cause. We saw this in 2009, when their struggle for an honest election was crushed in the streets. Most don’t hate the West.

Those voices can emerge if the regime is constrained and contained. Communist Russia, a nuclear superpower that under a different ideology also sought world dominion, was successfully contained until its regime collapsed. It is possible for America to contain the Islamic Republic. Iran’s would-be trading partners, who also want to keep doing business here, have reasons to cooperate. Ayatollah Khamenei could be contained, but not by underwriting his jihad through subsidies like the JCPOA.

Mr. Wambold is the grandson of the last Crown Prince and Shah (in exile) of the Qajar Dynasty of Iran, HIH Mohammad Hassan Mirza.