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On Monday Iraq’s army, assisted by Iranian forces, launched a major assault on the Kurds in the northern Iraqi city of Kirkuk. Across the length of America’s recent history with Iraq, we have had no more reliable ally than Iraq’s Kurds and their fighting force, the Peshmerga.

So far the Trump Administration has said little about the attack on the Kurds. “We’re not taking sides, but we don’t like the fact that they’re clashing,” President Trump told reporters at the White House Monday. “We’ve had, for many years, a very good relationship with the Kurds, as you know. And we’ve also been on the side of Iraq, even though we should have never been in there in the first place. But we’re not taking sides in that battle.”

But if the U.S. allows one of its most visible allies to be defeated in the Middle East, make no mistake: Other allies in the region will notice and start to recalculate their relationship with the Trump Administration.

The Iraqi Kurds, to be sure, have contributed to their current plight. Kurdish President Masoud Barzani went forward with a needless independence referendum last month, despite pressure from the U.S. not to hold the vote. The pro-forma vote gave the Baghdad government a pretext to play the nationalist card and retake Kirkuk.

Kirkuk is a multi-ethnic city that lies just south of Iraq’s Kurdistan, an autonomous region whose borders abut Iran and Turkey. The Kirkuk region is also rich in oil. The Kurds gained control of Kirkuk in 2014 after Iraq’s army famously fled under attack from Islamic State, which seized control of Mosul in June that year.

After the Iraqi forces abandoned the region, the Peshmerga became the primary reason that Islamic State was never able to consolidate its control of northern Iraq. Arguably, the Kurds, backed by U.S. air power, saved Iraq by giving Iraqi Prime Minister Haider al-Abadi time to reconstitute his nation’s army into a fighting force capable of driving Islamic State out of Iraq’s major cities, with the help of the Peshmerga.

Possibly the phrase “no good deed goes unpunished” originated in the Middle East. Having taken back Mosul from Islamic State, Mr. Abadi now wants to drive the Kurds back into their northern Iraqi homeland. But the strategic details of this attack on the Kurds are important. Iraq’s offensive includes Iran. According to the Washington-based Institute for the Study of War, Iranian-backed militias and the 9th Iraqi Armored Division moved toward Kirkuk last week to support the Iraqi army.

The Abadi government in Baghdad is under constant pressure from Shiite Iran to align itself against the interest of Iraq’s Sunni populations in the north and west. It follows that after Iraq’s progress on the battlefield against Islamic State, Iran would encourage the Iraqis to drive the Kurds out of Kirkuk.

Notice this is all happening within days of President Trump decertifying the Iran nuclear deal, based in part on the assumption that Europe will support U.S. efforts to resist Iran’s ballistic-missile program and its penetrations across the Middle East. But what will the Europeans or our allies in the Middle East conclude if we abandon one of our oldest regional allies, the Iraqi Kurds?

The U.S. no doubt has lost much of the political leverage it had before the Obama Administration pulled out of Iraq in 2011. But abandoning the Kurds to an Iraq-Iran Shiite alliance would only deepen U.S. losses.

Before Iraq and the Kurds go to war, the U.S. could insist that Iraq reaffirm the autonomy of Iraqi Kurdistan and also that it work out an agreement to share revenue from the region’s oil reserves. The alternative to such a modus vivendi for Prime Minister Abadi is a capable Kurdish fighting force in a state of permanent insurrection.

The U.S. owes a debt to the Kurds. Abandoning them now would damage America’s credibility, and not least Mr. Trump’s ability to enlist allies against Iran’s expansion across the Middle East. The assault on Kirkuk matters.