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Details on the trip are not yet public, but it represents a chance for Pence to smooth over relations with US allies who are adjusting to President Donald Trump's new leadership style and to discuss Trump's decision to pull out of the Trans-Pacific Partnership, a deal that would have included Japan and Australia.
By going to Indonesia, Pence will also be visiting the largest Muslim nation in the world amid the Trump administration's crackdown on refugee travel and immigration from six Muslim-majority countries.
The senior aide declined to get into specifics on Pence's trip to Indonesia, but Indonesian leaders have expressed their displeasure with the travel ban.
The senior Pence aide said the vice president is headed to Japan to discuss the economy.
Pence will look for "ways to strengthen the economy in Japan and the United States" while visiting the US ally, the aide said.
Prime Minister Shinzo Abe accepted Pence's offer to visit Japan early in the Trump administration when the prime minister visited the US in February, the aide added.
Pence's visit to South Korea comes amid turmoil in the country. South Korean President Park Geun-hye's impeachment has led to widespread rioting and uncertainty about the country's future political leadership.
It also comes at a time when North Korea has been, in the eyes of some experts, testing Trump with a series of ballistic missile tests. North Korean media said earlier this month that the launch of four missiles was meant to test the country's ability to hit US bases in Japan.
Secretary of State Rex Tillerson will visit South Korea this week.
Pence's Australia visit will come months after Trump had a tense call with Australian Prime Minister Malcolm Turnbull. Trump, according to sources, objected to an agreement over the US receiving refugees from Australia during the call and abruptly ended the call because he was unhappy with the deal.
He later tweeted about the agreement: "Do you believe it? The Obama Administration agreed to take thousands of illegal immigrants from Australia. Why? I will study this dumb deal!"