Pence spoke as he visited the recently expanded Panama Canal, whose construction was overseen by Roosevelt prior to its opening in 1914.
"In President Donald Trump, the United States again has a president whose vision, energy, and can-do spirit is reminiscent of President Teddy Roosevelt," Pence said.
"Then, as now, we have a builder of boundless optimism, who seeks to usher in a new era of shared prosperity."
Trump faced a political firestorm this week after he seemed to draw a moral equivalence between white supremacists who marched in Virginia and counter-protesters denouncing racism.
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Pence was wrapping up a tour of Latin American countries to boost trade ties and rally them over the crisis in Venezuela.
He cut short his stop in Panama by a day in order to get to Camp David for security talks on Afghanistan on Friday.
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