It appears that every public appearance by Donald J. Trump produces a signature line, one that provokes astonishment and disbelief.

The other day he held that wild-and-woolly press conference in which he declared he scored the greatest Electoral College win since Ronald Reagan. It was false.

Then he jetted off to Melbourne, Fla., for a campaign-style rally. He baited his worshipers with more promises to end “radical Islamic terrorism.” Then he singled out Sweden — Sweden! — as a place that had been victimized by terrorists.

“You look at what’s happening in Germany, you look at what’s happening last night in Sweden — Sweden, who would believe this?” Trump bellowed during his rally.

The remark provoked astonished expressions from the Swedes. What? Huh? Terrorist attack? Where? By whom?

Of course, there was no such terror attack in Sweden. Trump made it up. He improvised yet another riff that produced — once again — the kind of thoughtless, careless and reckless rhetoric from the commander in chief.

Each time he does this, the president undermines the nation’s standing, let alone the standing of the high and (formerly) dignified office he occupies.

And what about our relationship with Sweden, a nation that has been famously neutral in world conflicts, but which remains an important ally of ours? Do the Swedes trust the U.S. president? Can they trust him to speak with clarity and precision?

For that matter, can we Americans trust the president?