Mr. Pence’s disciplined delivery of the American message after the Syria strikes stood in contrast to the presidential tweet, which recalled an earlier president’s premature declaration of victory in Iraq and prompted a spate of bitter criticism.

What the president had meant by his tweet, Mr. Pence explained to reporters traveling with him on Saturday, was that the mission that Mr. Trump had given American forces, “to go in and destroy key elements of the chemical weapons infrastructure in Syria, was completely and professionally and swiftly accomplished.”

But that was not the only issue on which Mr. Pence worked to modulate Mr. Trump’s pronouncements here. In a meeting with President Enrique Peña Nieto of Mexico, the vice president said, he steered clear of talking about funding for the border wall that Mr. Trump has long demanded Mexico pay for. Mr. Pence chalked up the disagreement — which recently torpedoed plans for a White House meeting between Mr. Trump and Mr. Peña Nieto — to two presidents with “strong personalities.”

“When you have two people with strong personalities, they occasionally have strong differences,” Mr. Pence told reporters. “We talked through those differences, some of which we set aside for a later date.”

Instead, Mr. Pence accentuated the positive: namely, progress in the renegotiation of the North American Free Trade Agreement with Canada and Mexico, which he said had a chance of being successfully completed within weeks.

As Mr. Pence taxied for takeoff on Air Force Two on Friday for the trip to Lima, the president appeared to be focused elsewhere. He tapped out a tweet branding James B. Comey, the former F.B.I. director whose forthcoming memoir paints him as a liar and Mafia-style bully, “an untruthful slime ball.” Privately, Mr. Trump continued to seethe over the F.B.I. raid days earlier on his personal lawyer in a wide-ranging corruption investigation that he views as a grave threat.

At the summit meeting in Peru, Mr. Pence spoke in loftier terms, trying to reassure the other leaders that Mr. Trump meant no slight in failing to show up for their gathering. Mr. Trump, he told President Juan Manuel Santos of Colombia, was “disappointed” that he could not make the trip — which was to have included a stop in Bogotá to meet with Mr. Santos — but, he added, “I can assure you that the relationship with our country has never been stronger.”