The ink — likely the disappearing kind — barely had time to dry on a deal that let the leading Russian mutineer off the hook when a notorious Iranian police chief landed at Moscow on Monday. Did the Islamic Republic’s top cop come to learn how to put down an uprising, or teach it?

As a plane linked to the Wagner group’s chief, Yevgeny Prigozhin, landed at Minsk after a deal that allowed him to live — at least for now — a plane arrived at Moscow carrying the Islamic Republic’s law enforcement chief, Brigadier General Ahmadreza Radan. 

President Putin’s initial shaky reaction to what he called a mutiny, and his seemingly soft approach in the aftermath of Wagner’s show of force, raised some eyebrows at Tehran. As Mr. Prigozhin marched Saturday, challenging Mr. Putin’s authority, official Iran, at least initially, seemed noncommittal. 

Iran “supports the rule of law in the Russian Federation,”  the Iranian foreign ministry spokesman, Nasser Kanani, said, pointedly avoiding a mention of Mr. Putin’s name. The foreign minister, Hossein Amir-Abdollahian, called his Russian counterpart, Sergey Lavrov, but he too merely expressed the hope that “Russia will overcome this phase.”

Some legislators and commentators were outright critical. Mr. Putin paid the price of “relying on mercenaries,” a political analyst, Ahmad Zeidabadi, tweeted. Fighters deployed to foreign countries could “one day turn their weapons to the internal front,” a former culture minister, Abbas Salehi, added. “Wagner is an example. Will we learn a lesson?!”

Then, officials quickly turned to full-throated support of Mr. Putin. Legislators and commentators “say all kinds of things,” the policy director at United Against Nuclear Iran, Jason Brodsky, tells the Sun. In the end, though, the supreme leader, Ali Khamenei, has “made a strategic decision to ally with Russia, and that will not change anytime soon.”

Iranians with long historic memories may be wary of alliances with Russia. In the 1820s the two countries fought a bloody set of wars that ended with the treaty of Turkmenchay. Persia ceded to tsarist Russia vast territories that Tehran formerly controlled in the Caucasus, including today’s Armenia, Azerbaijan, and parts of modern Turkey. 

Currently, though, Tehran and Moscow are allied in a revanchist axis that cooperates around the globe to undermine America and its allies. Fighters from the Islamic Revolutionary Guard Corps and an Iranian proxy, Hezbollah, battle in Syria alongside Wagner mercenaries. 

Perhaps that blood-brother alliance explains Tehran’s initial bet-hedging: Who would you side with — Mr. Prigozhin, who commands your Syrian allies, or Moscow’s strongman, Mr. Putin? 

Official Tehran tends to support despots in allied countries, an Iran watcher at the Foundation for Defense of Democracies, Behnam Ben Taleblu, tells the Sun. The mullahs have sided with President Assad of Syria throughout the civil war, as well as with President Erdogan of Turkey in the 2016 coup, for two.

Iran is likely to keep its ties with Russia regardless of which strongman ends up in the Kremlin. Moscow has stood with Tehran at the United Nations Security Council and other diplomatic fora, and Mr. Khamenei now rewards it by aiding Mr. Putin’s Ukraine war.

The drones Iran sells Russia are proving essential for Moscow. In return, Moscow is now contemplating sending items that could advance Iran’s nuclear program. “The partnership with Russia will go on regardless of Putin’s future,” Mr. Brodsky says. “I expect the arm shipments to continue.”    

That said, “ruling Iran hardliners were greatly concerned by the Wagner uprising in Russia,” an Iran watcher at Israel’s Reichman University, Meir Jefandefar, tweeted. “That Iran sent the head of its police force to Russia today attests to that. In Iran, the police are the first line against mass domestic uprisings.”

General Radan plans to “hold talks with Russian police officials and sign a memorandum of cooperation between the police forces of the two countries in the fight against terrorism, human trafficking and drugs, and also in scientific and research fields,” the semi-official Tasnim news agency reported Monday.

The Islamic regime has been brutal in suppressing a popular uprising since last September, when a young Kurdish Iranian, Mahsa Amini, died in custody for allegedly wearing her head covering improperly. Before that, several popular protests were quashed by regime enforcers. Mr. Putin’s enforcers have also managed to cruelly end challenges to his authority. 

Yet, Mr. Putin’s inept handling of the short-lived Wagner coup attempt indicated that Moscow may now require a refresher course in ending domestic unrest. As General Radan comes calling, Tehran seems “eager to transfer to Putin lessons about paramilitary command and control against local populations,” Mr. Ben Taleblu says. 

Mighty Russia was once the senior partner in the relationship. Now, the Islamic Republic imparts advice on oppressing crowds, and Tehran is Russia’s arms supplier. “The Venn diagram between Putin and Khamenei is moving closer to being two overlapping circles,” Mr. Ben Taleblu says.