Bush's five-hour trip to the southern city of Hyderabad came a day after he sealed a landmark civilian atomic cooperation deal with New Delhi that recognizes India's status as a responsible nuclear power.
"People do lose jobs as a result of globalization. And it's painful for those who lose jobs," Bush told an entrepreneur during a discussion at Hyderabad's Indian School of Business.
The United States would counter it by educating people to acquire the skills needed forrather than discouraging outsourcing, he said.
"The United States will reject protectionism. We won't fear competition. We welcome competition, but we won't fear the future either because we intend to shape it through good policies," Bush said.
"People in America should, I hope, maintain their confidence about the future," said Bush, whose job approval ratings have been tumbling in part because of concerns about the U.S. economy.
Outsourcing and software exports arein the fiscal year ending March, with about 60 percent of that coming from U.S. companies.
As Bush spoke, hundreds of Muslim youths fought pitched battles with policemen outside a mosque about 10 miles away in the city's old quarters, throwing stones and bricks as they protested against his visit.
Four people including two policemen were injured as police caned the demonstrators, an officer said.
A Muslim man was shot dead in the northern Indian city of Lucknow as protests spun out of control and triggered communal clashes with Hindus, police said.
The trouble started when Hindus refused to heed a call by Muslim demonstrators to close shops, leading to riots in which stones were hurled at shops, vehicle windscreens smashed and property burned, they said.
Meeting the buffalo
Traffic was very sparse in the usually choked streets and bylanes of Hyderabad's old quarters as markets and businesses shut down in protest.
"Osama is our ideal, we can die for Osama," shouted some Muslim engineering students as they marched through the streets carrying posters of al Qaeda leader bin Laden.
"He is a freedom fighter. He is our leader. We love him more than our parents," said Mohtassin, a 19-year-old student who gave only one name.
Protests were also staged in the capital New Delhi, the northern city of Lucknow and Srinagar, the summer capital of Jammu and Kashmir state, India's only Muslim-majority state.
Earlier, Bush visited an agriculture university and toured the seed research area where women in sarees bent and tended to green patches where peanuts and soybeans had been planted.
The university began collaborating with Cornell University of the United States in 2004 to develop Indian agriculture.
Bush was also shown a huge, black Indian buffalo and university officials wanted a farmer couple to milk the animal with their hands in front of the visitor but the U.S. president was apparently not keen to see it, officials said later.
Security for Bush in the region has been stepped up.
In Pakistan, the president's next stop, a suicide bomber killed an American diplomat and two others outside the U.S. consulate in Karachi on Thursday.
Bush said terrorists would not stop his Pakistan visit, where he is due to hold talks on Saturday.
The nuclear deal, which would make U.S. nuclear fuel and technology available to New Delhi despite concerns in the United States, put the seal on Bush's India visit.
But it still needs to be endorsed by the U.S. Congress and, in an indication of possible rough water ahead, a leading Democrat called the pact a "historic failure."