MUMBAI, India - A relaxed President Barack Obama on Sunday showcased the softer side of his agenda in India, soaking in a celebration of a revered festival and telling science-loving students: "We are very proud of you."

Stepping back briefly from the economic mission of his visit here, the president and his wife, Michelle, stopped by a local school for a joyous performance in honor of Diwali, celebrated by Hindus and Sikhs as a victory of good over evil. The first lady eagerly danced with the children, acquitting herself well. The president eventually got up and gave it a go.

The happy imagery is part of Obama's outreach to this democracy of more than 1 billion people, an emerging power in Asia and increasingly important partner to the U.S. on matters of trade and security. Obama was to meet with farmers, hold a town hall with college students and then head for more events in the capital of New Delhi.

At Holy Name High School, the Obamas smiled and chatted with youngsters. First came a detailed explanation of environmental projects by children, impressing Obama, always a promoter of studies in the field of science.

"Outstanding," the president declared. The Obamas then took part in a candle-lighting ceremony and watched girls in colorful garb of blues, greens, pinks and orange perform a swaying dance with graceful hand gestures.

A final, lively performance got Mrs. Obama up, twirling and bouncing with students on the dance floor. The kids eventually pulled up a more rigid president up to dance, enshrining a memorable image of his long journey to Asia.

Obama is in the midst of 10 days of travels to India, Indonesia, South Korea and Japan.

On Saturday, Obama embraced India as the next jobs-creating giant for hurting Americans, not a cheap-labor rival that outsources opportunity from the U.S.

Fresh off a political trouncing at home, Obama was determined to show tangible, economic results on his long Asia trip, and that was apparent from almost the moment he set foot on a steamy afternoon in the world's largest democracy. By the end of the first of his three days in India, he was promoting $10 billion in trade deals - completed in time for his visit - that the White House says will create about 54,000 jobs at home.

That's a modest gain compared with the extent of the enduring jobless crisis in the United States. Economists say it would require on the level of 300,000 new jobs a month to put a real dent in an unemployment rate stuck near 10 percent.

Yet to Obama, the bigger picture was the lucrative potential of an unleashed trading relationship between India and the United States. He seemed comfortable and energized away from Washington, days removed from the GOP's election thumping.

"For America, this is a jobs strategy," Obama said of his emphasis on trade, although it could stand as a motto for his 10-day trip. He was spending Sunday with young people in Mumbai and then heading onto meetings in New Delhi, the capital, before shifting later in the week ahead to Indonesia and economic talks in South Korea and Japan,

In India for the first time, Obama quickly got a sense of riches and poverty, history and tragedy.

His helicopter ride into this bustling financial center took in some of the country's slums. His luxury accommodation for the night, the Taj Mahal hotel, was one of the sites of a terrorist rampage in Mumbai that killed 166 people. Obama and his wife paid quiet tribute to the 31 people slain at the hotel, looking over their names inscribed in a memorial before meeting with victims' families and survivors of the shootings.

"We visit here to send a very clear message that in our determination to give our people a future of security and prosperity, the United States and India stand united," Obama said from an outdoor plaza, the soaring Gateway of India and the Arabian Sea behind him. "We'll never forget."

Indian commentators seized on the president's failure to mention Pakistan, India's neighbor and bitter rival. Pakistan was home to the 10 assailants.

The president also celebrated the life of a personal hero, Mohandas K. Gandhi, a father of Indian independence and model of peaceful activism. The Obamas spent time at the home-turned-museum where Gandhi once lived. They signed personal messages into the guest book and pledged to bring their daughters, Sasha and Malia, back one day.

Obama directly addressed the belief in the U.S. that India is robbing Americans of jobs. He acknowledged that many Americans only know trade and global commerce as the source of a job shipped overseas.

"There still exists a caricature of India as a land of call centers and back offices that cost American jobs. That's a real perception," Obama said. He noted the real concern in India that American corporate giants, if welcomed, would run mom-and-pop stories out of business and upend Indian culture.

Seeking to dismiss all "old stereotypes," Obama said the relationship between the countries is "creating jobs, growth, and higher living standards in both our countries. And that is the truth."

In the fallout of the U.S. elections, in which Democrats lost control of the House and Obama's ability to connect with his country was called into doubt, the president said one lesson learned was the need to set a better tone with business leaders. He was effusive on that front in Mumbai, gathering with top U.S. executives and studying up on their commerce with India.