The U.S. will provide $16 million in aid to Venezuelans who have fled their homeland amid a growing humanitarian and economic crisis, Vice President Mike Pence said Friday as he arrived in Peru for a day of talks with Latin American leaders.

“We are with the people of Venezuela and will continue to do everything in our power to provide sustenance and support to those who have fled,” Mr. Pence said. The U.S. funds will go to the United Nations High Commissioner for Refugees and on to communities in Colombia and Brazil flooded...