Early Friday morning, President Trump tweeted, “Iran is playing with fire — they don’t appreciate how ‘kind’ President Obama was to them. Not me!”

Earlier in the week, both the president and National Security Advisor Mike Flynn said they were putting Iran “on notice,” without defining what that notice meant. Mr. Trump likes to keep our adversaries guessing, and that’s a good thing, if he actually does it.

More definitively, a statement by Flynn said, “The days of turning a blind eye to Iran’s hostile and belligerent actions toward the United States and the world community are over.” For the moment, it appeared as if they’ve drawn an Obama-esque “red line” in the waters of the Gulf of Aden.

The events leading up to these began a few days earlier on January 29. On that day, a raid on al-Qaida in Yemen killed a few of the bad guys and resulted in the death of William “Ryan” Owens, a SEAL Team 6 operator. On the same day, Iran test-fired a medium-range nuclear-capable ballistic missile. This was its 12th launch since Obama’s nuclear agreement came into effect in October 2015.

The next day, Iran’s Houthi rebel surrogates in Yemen nearly destroyed a Saudi Arabian frigate in the Gulf of Aden in a suicide boat attack much like the one that nearly sank the USS Cole in the Yemeni harbor of Aden in October 2000. The repaired USS Cole is now reportedly on patrol nearby, a clear taunt at the Houthi rebels and Iran.

The president’s response has so far been limited to sanctions on a dozen companies (Chinese, Lebanese, and Emirati) and 13 individuals, freezing their assets in the United States.

Mr. Trump has been in office two weeks and three days, so it’s too early to judge his response to Iran’s actions or the strategy he is developing. Flynn’s statement indicates that more — maybe a lot more — is coming.

Messrs. Trump, Flynn, and Mattis don’t have many good options. There hasn’t been a direct provocation justifying military action. They can’t claim that the Iranian launch violates U.N. Security Council Resolution 2231 because, under its terms, which blessed Obama’s nuclear deal, Iran’s missile program is not at all limited. Iran is only discouraged from doing things that increase regional instability. “Discouraged” isn’t defined as “prohibited” in anyone’s dictionary.

We can only guess where the president means to go, but we can discern some of the facts that limit him. He got it a bit wrong by saying Iran is playing with fire: The ayatollahs are playing in fire, reveling in it, as they have since they seized our Tehran embassy in 1979. And so have the Russians going back to the 17th-18th century rule of Peter the Great, whose portrait hangs in a prominent spot in Mr. Putin’s office.

Mr. Trump knows of the Russian actions that have brought about a serious flare-up of fighting in eastern Ukraine. The Ukraine fighting will wax and wane, and he should know that the Ukrainians’ calls for help have so far been ignored. No lethal aid has yet gone to the Ukrainians even though legislation authorizing it was passed in 2015. Such aid should commence forthwith.

Mr. Trump is caught between his wish for a partnership with Mr. Putin in fighting ISIS and Putin’s actions in Ukraine. The new round of fighting there began only hours after a conversation between the two leaders. It’s a rather unsubtle test of Mr. Trump’s intentions by Mr. Putin. If we continue our failure to send lethal aid to Ukraine, Mr. Putin will become confident that Mr. Trump values his “friendship” far too highly.

Similarly, Mr. Trump’s new strategy against Iran has to account for Russia’s involvement in Syria and its all-too-effective alliance with Iran. To be perfectly clear, Mr. Trump would be foolish in the extreme to trust Mr. Putin in any respect.

Yet that investment of trust seems to be Mr. Trump’s fondest wish. In a pre-Super Bowl interview with Fox News’ Bill O’Reilly, Mr. Trump was challenged on precisely this point. When the two spoke about Mr. Putin, Mr. O’Reilly challenged the president by saying that Mr. Putin is “a killer.” As reported by the Washington Post, Mr. Trump responded:

“There are a lot of killers. We have a lot of killers,” Trump said. “Well, you think our country is so innocent?” Mr. Trump added that he thinks the United States is “better” getting along with Russia than not.

“If Russia helps us in the fight against ISIS, which is a major fight, and Islamic terrorism all around the world, major fight. That’s a good thing,” Mr. Trump said.

By that statement, the president granted moral equivalence between the United States and Mr. Putin’s Russia, which assassinates journalists and political opponents, subjugates neighboring states (and continues to attempt to subjugate Ukraine), and is Iran’s principal ally in attempting to conquer the Middle East.

Mr. Trump’s statement risks him being included among the people Joseph Stalin called “useful idiots.” It was an enormous mistake for two reasons.

First, that statement confessed Mr. Trump’s belief that we are dependent on Mr. Putin’s help in the coming campaign to destroy ISIS. He thus prejudged Mr. Mattis’s strategy before it’s drafted.

Second, by granting moral equivalence between Russia and the U.S., Mr. Trump made it harder to deal with both Russia and Iran. It was precisely the kind of confession of intentions he abhors.

The experts have always insisted that Tehran calibrates its actions to avoid a serious response from us. But they’ve ignored one important fact: that aside from the Stuxnet cyberattack of 2010, Iran has never been punished for its actions and, in that case, the Iranians made no aggressive response. In the meantime, it is — as Mr. Mattis said recently — the world’s principal state sponsor of terrorism. It is obviously developing intercontinental missiles as well as nuclear weapons for the missiles to carry.

In short, we have trained Iran to ignore our warnings and have only once, for a brief time, interrupted its march toward domination of the Middle East. Similarly, Russia was trained by Mr. Obama that its aggression in Europe and the Middle East will be met with only words rather than action.

Mr. Putin’s Russia and the ayatollahs’ Iran both have centuries-long histories of opportunistic aggression and conquest. Both have made their choice. Iran’s regime has committed its religious fervor to the development of nuclear weapons and the missiles to deliver them. Mr. Putin’s regime — despite Russia’s increasingly weak economy — depends on aggression to survive by stirring nationalistic fervor to feed Russia’s historic paranoia.

So what to do about Iran and Russia?

Mr. Obama’s nuclear weapons deal contains nothing that in any way limits what Iran can do or what Russia can do to help Iran. Mr. Trump would do better by divorcing us from it as he promised during his campaign.

Iran already has several billion dollars in cash, as a result of the deal. U.S. companies, such as Boeing, are making deals for multi-billion dollar sales to Iran. The NATO nations are doing the same. None of those deals should be effectuated, but they may prove impossible to stop. Mr. Trump may be able to force Boeing to cancel its deal, but Airbus, the European aircraft manufacturer, would step in instantly to take the Boeing deal for itself.

And forget the U.N. There will be no “snap back” of international sanctions on Iran, because Russia and China (and probably France) won’t agree to them.

Mr. Trump could bar Iranian banks from clearing U.S.-dollar transactions through American banks. That would, in a year or two, fail because the Chinese are waiting eagerly to replace the dollar as the international reserve currency. They, the Russians, and the Europeans will step in.

Mr. Trump should encourage the Saudis to use their military power to put down the Houthi rebellion in Yemen. They probably won’t, because they don’t want to take on Iran even indirectly by taking out its surrogates. We shouldn’t do it for the Saudis, who are waiting to see if Mr. Trump will do what previous presidents have done and fight the Saudis’ wars.

But telling the Saudis to get on with it should be part of his strategy because it would show our faux-allies such as the Saudis that we are serious about stopping Iran’s aggression. They should have to undertake to destroy the Houthi rebellion and Iran’s presence in Yemen.

Mr. Trump said all options are on the table. We can begin with an intensive cyberwar against Iran. That would mean interfering with everything from future missile launches to disrupting Iranian bank operations. We should be doing this every day, with every tool at our disposal.

When Israeli Prime Minister Netanyahu visits the White House later this month, Mr. Trump should offer him the arms Mr. Obama denied the Israelis, including the deep-penetrating bombs that would threaten Iran’s hardened nuclear sites. He should also offer whatever aid the Israelis need to improve their Arrow anti-missile systems.

In 2009, Mr. Obama failed to come to the aid of Iranian rebels who had, at the time, a good chance of toppling the ayatollahs’ regime. Mr. Trump should secretly make it known to whatever rebels still desiring to overthrow the ayatollahs that we will not fail to come to their aid.

To deal with Russia successfully, Mr. Trump needs to stop speaking in terms of U.S. dependency on Russian goodwill. Russian cooperation in destroying ISIS can’t be the keystone of the strategy that Defense Secretary Mattis is crafting now.

America always stands for freedom. Both the Iranian ayatollahs and Mr. Putin’s Russia stand against it. Mr. Trump needs to say so in loud and clear terms. Mr. Trump will eventually come to understand that. But “eventually” may take too long to come.