Pence was speaking in the world's most populous Muslim nation midway through a 10-day swing in Asia meant to reinforce key US alliances at the start of the Trump administration. He met with the country's president, Joko Widodo, and toured the largest mosque in the region.
Pence said the US would continue working with Indonesia to combat terrorism, and said the country's form of Islam should serve as an example to other nations.
"As the largest majority Muslim country, Indonesia's tradition of modern Islam, frankly, is the inspiration to the world," he said. "We commend you and your people. In your nation as in mine, religion unifies -- it doesn't divide. It gives us hope for a brighter future. And we're all grateful for the great inspiration that Indonesia provides for the world."
The Trump administration has caused concern among the world's Muslims for some of its proposals, including barring entry to citizens of some predominantly Muslim nations. That plan, however, remains stalled in courts and hasn't gone into effect.
Nonetheless, the proposed entry ban has caused consternation in some countries. On Wednesday, the Dubai-based airline Emirates said it was reducing US-bound flights after interest waned, citing the ban as a contributing factor.
"The recent actions taken by the US government relating to the issuance of entry visas, heightened security vetting, and restrictions on electronic devices in aircraft cabins, have had a direct impact on consumer interest and demand for air travel into the US," Emirates said in a statement.
As a candidate, President Donald Trump proposed disallowing entry to all Muslims into the United States for security reasons. His campaign website still has a statement saying Trump was "calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."
Pence, in Jakarta, said Trump was not interested in banning entry to all Muslims.
"Rest assured, under President Trump, the United States welcomes all who share our values for that brighter future," he said.
He also announced Trump's intentions to visit Southeast Asia in November for a yearly set of conferences. The summits this year take place in Vietnam and the Philippines, where President Rodrigo Duterte has led a violent crackdown on drug dealers.