The congressman from Indiana reminded his colleagues of the necessity of “confronting tyranny.” He affirmed that he stood with President George W. Bush. And he declared Baghdad, simply, as “guilty.”

“It has come from time to time upon the free nations of the world, and it seems most especially on the United States of America, to be willing to employ the arsenal of democracy to confront force with force as a last resort,” the congressman, Mike Pence, told his fellow representatives in a speech shortly before the 2003 invasion of Iraq. “And we may well become upon such a time again.”

As the fighting continued year after year, Mr. Pence kept up his support, speaking forcefully in favor of the Iraq war even as many Americans turned against it. But his firm stance on that invasion now represents one of the most jarring differences in his abrupt political marriage to Donald J. Trump, who has repeatedly emphasized his opposition to the war.

From the use of force to free trade to diplomacy, Mr. Trump and Mr. Pence hold very different views of the United States’ role in the world, and reconciling them as they enter the heart of the campaign may prove to be a challenge.