Obama's trip -- coming just days after Republicans reclaimed the House of Representatives and dented the Democratic majority in the Senate -- has been criticized by analysts, who say it allows Republicans to set the message at home while he is abroad.
Obama was to meet with U.S. military officials during a refueling stop in Germany, where he exited Air Force One for a short time.
Administration officials told reporters just before the refueling stop the president's main meeting in India with business leaders will include more than 200 American business executives, including executives from General Electric Co. and PepsiCo Inc..
India is the first leg of his trip, which includes a Group of 20 summit in South Korea, an Asia-Pacific Economic Council conference in Japan, bilateral meetings with at least six leaders, as well as major speeches, public appearances and news conferences.
The main purpose the trip "is to take a bunch of U.S. companies and open up markets so that we can sell in Asia, in some of the fastest-growing markets in the world, and we can create jobs here in the United States of America," Obama said Thursday.
He also said he hoped there would be some "specific announcements that show the connection between what we're doing overseas and what happens here at home when it comes to job growth and economic growth."
Asian countries are "serious about competing," he said. "They are serious about competing with us not just on manufacturing but on services. They're competing with us when it comes to educational attainment, when it comes to scientific discovery."
The White House has called claims by conservative Republicans that the trip was costing $200 million a day "wildly inflated," but would not provide a price tag for the visit.
The administration considers the U.S.-India relationship a "defining partnership of the 21st century," Bill Burns, the undersecretary of state for political affairs, said during a background briefing on the trip.
"The simple truth is that India's rise and its strength and progress on the global stage is deeply in the strategic interest of the United States," Burns said. "We're the world's two largest democracies. We're both big, diverse, tolerant societies. We're two of the world's largest economies. We both have an increasing stake in global stability and prosperity, especially across Asia and the Pacific."
A recent trip to India found the mood there positive, Burns said, adding there was "an air of anticipation, a lot of interest in how we can work together to translate all the progress of recent years into the sort of further tangible benefits that both Indians and Americans can see."
Burns, White House spokesman Robert Gibbs and others avoided direct discussion on the outsourcing of U.S. jobs to India in the face of a dismal unemployment reports at home.
"I would simply say that a key part of the message is going to be that we want to make sure (there are) opportunities for U.S. jobs, U.S. exports," said Ben Rhodes, deputy national security adviser for strategic communications.
While in Mumbai, Obama and first lady Michelle Obama will stay at the Taj Hotel, one of the targets of terrorists who attacked India's financial and entertainment hub in November 2008. He also will visit New Delhi.
"The president wanted to take the time to pay his respect to the victims who lost their lives and to sign the guest book there," Rhodes said.
Obama will visit the Gandhi Museum, attend the U.S.-India Business Council summit, visit a school to help celebrate the Diwali holiday and participate in a town hall with university students.
"We believe that Asia is critical to our foreign policy strategy. It's the fastest-growing markets in the world. It's fundamental to our export initiative," Rhodes said. "So India is a cornerstone of our broader Asia approach, which is focused on, again, expanding exports for U.S. goods, deepening partnerships in important part of the world (and) partnering together in the (Group of 20) and other forums."