WASHINGTON — For 55 minutes, with cameras rolling, President Trump engaged in a vigorous discussion of immigration with congressional leaders of both parties in a setting usually reserved for bland talking points and meaningless photo opportunities.

In effect, the president and his visitors threw away the blah-blah scripts and negotiated possible legislation in front of the nation. “I hope we’ve given you enough material,” a pleased Mr. Trump joked with reporters as he finally ushered them out of the Cabinet Room in the White House.

That was the point. After days in which his very fitness for office was debated, Mr. Trump appeared intent on demonstrating that he could handle the presidency. He was in command of the meeting while inviting input. He did not berate anyone. He did not call anyone derogatory nicknames. He signaled that he was open to compromise.

The bar, of course, was historically low given that Democrats and even some Republicans have been describing him as so unstable that he should be removed from office. For his advisers, the meeting was a relief, a chance to reset the narrative and make Mr. Trump look more like a traditional president. And his critics, grading on a curve, called it a welcome change, a moment of constructive engagement that they hoped would lead to more.