Pence expects to talk about the "belligerence" of North Korea at stops in Tokyo, Jakarta and Sydney, the White House adviser said.
But the need for "free and fair trade" will also be a theme, the adviser said.
Trump campaigned on an "America First" trade policy, complaining that trade partners in Asia and elsewhere had taken advantage of the United States.
One of his first acts in office was to remove the United States from the 12-nation Trans-Pacific Partnership (TPP) trade deal negotiated by former President Barack Obama.
"Withdrawing from the TPP shouldn't be seen as a retreat from the region. On the contrary, our economic presence in the region is enduring," the adviser said.
On Tuesday, Pence will kick off economic talks with Japan requested by Trump and Prime Minister Shinzo Abe. The discussions will focus more on setting a "framework" for future talks rather than on specific industry issues, a White House official said.
Pence will meet with business leaders at each stop, including in Jakarta, though he was not expected to wade into the weedy details of disputes between the Indonesian government and U.S. companies like mining giant Freeport-McMoRan.
"We're going to discuss the business environment in Indonesia in a general sense," a White House official said.