A decade and a half ago, in the run-up to the invasion of Iraq, President George W. Bush’s administration conjured up not only terrifying images of nuclear mushroom clouds but also of Saddam Hussein plotting with Osama bin Laden to attack the United States.

Mr. Bush himself declared that Mr. Hussein “aids and protects terrorists, including members of Al Qaeda” while Secretary of Defense Donald Rumsfeld called links between Iraq and Al Qaeda “accurate and not debatable.”

It wasn’t true, of course. But it helped make the case for war.

That may be why a similar lie is getting trotted out again now, except this time the target is Iraq’s neighbor, Iran.

On Oct. 13, in his statement decertifying the Iran nuclear deal, President Trump claimed that Tehran “provides assistance to Al Qaeda.” The following week, his C.I.A. chief, Mike Pompeo, went further: “It’s an open secret and not classified information that there have been relationships, there are connections,” Mr. Pompeo said at an event hosted by the Foundation for Defense of Democracies, a neoconservative think tank. “There have been times the Iranians have worked alongside Al Qaeda.”