MUMBAI, India – President Obama, challenged by Indian students Sunday to explain why the United States had not labeled Pakistan a terrorist state, defended his administration’s efforts to help the Pakistani government root out extremism and urged Indians to remember their own stake in promoting stability in their longtime rival nation.

Obama’s call for India to make a gradual rapprochement with Pakistan, made during a town-hall style meeting at St. Xavier’s College in the city of Mumbai, is likely to be repeated today to the Parliament in New Delhi.

A day earlier, Obama met with survivors of the 2008 terrorist attack on Mumbai by Pakistani extremists, but he was careful to avoid mentioning Pakistan.

On the second day of a 10-day Asia trip, he was clearly ready for more direct engagement on the matter. “I was expecting it,” he said, eliciting laughter from the college audience.

Obama said the U.S. approach toward Pakistan on the issue of terrorism has been “to say we are your friend, this is a problem and we will help you with it, but the problem has to be addressed.”

He said he was “absolutely convinced that the country that has the biggest stake in Pakistan’s success is India.”

“So my hope is, is that over time trust develops between the two countries,” he said, “that dialogue begins and that over time there’s a recognition that India and Pakistan can live side by side in peace and that both countries can prosper.”

India was partitioned to create Pakistan at the time of independence from Britain in 1947, and the two neighbors have fought three major wars since.

Indian students also asked him about his views on jihad and Afghanistan policy, but Obama kept at least a part of his message focused on the main aim of his second extended trip to Asia: opening up markets to create job opportunities for Americans.

On Sunday, he told students that Americans were frustrated with the U.S. economy and how the midterm election results had forced him to make “some midcourse corrections and adjustments.”

“So I want to make sure that we’re here because this will create jobs in the United States and it can create jobs in India,” Obama said. “But that means that we’ve got to negotiate this changing relationship.”

Some listeners were skeptical, aware that Obama and other Democrats often speak disapprovingly of U.S. companies that “ship jobs overseas.” India has long been a favored destination for American outsourcing of data processing, call centers and back-office functions.

“It hurts us,” said Lopa Mullick, an owner of an events-management company. “You’re not looking at all the opportunities that India has created for the U.S., at the economic benefits both sides get.”

Still, the young entrepreneur said she came to listen to Obama because she believes he can “shift the focus” and that he may actually want to do so.