Bush's five-hour trip to the southern city of Hyderabad on Friday came a day after he sealed a landmark civilian atomic cooperation deal with New Delhi that recognises India's status as a responsible nuclear power.
Bush told an entrepreneur during a discussion at Hyderabad's Indian School of Business that "people do lose jobs as a result of globalisation. And it's painful for those who lose jobs".
The United States would counter job losses by teaching people new skills rather 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, partly because of concerns about the US economy.
Later on Friday, Bush left India and arrived in Pakistan amid tight on the final leg of his South Asian tour, an official said.
The US president landed at an airbase in Rawalpindi, near the Pakistani capital Islamabad, Pakistan's Foreign Ministry spokeswoman Tasnim Aslam said.
Outsourcing and software exports are forecast to earn India more than $20 billion in the fiscal year ending March, with about 60% of that coming from US companies.
The boom has created millions of jobs along with consumer demands that have attracted American businesses.
A luxury goods market has emerged, with brands like Louis Vuitton and Rolls Royce setting up shop along with consumer demands that have attracted American businesses.
Though 80% of Indians live on less than $2 a day, India's middle class has swelled to a number larger than the population of the entire US.
Hundreds of leftist and Muslim
protesters criticised Bush
The US trade deficit with India nearly doubled, to $10 billion, from 2001 to 2005.
As Bush spoke, protests by communists and Muslims were held elsewhere in the city.
Hundreds of Muslim youth fought pitched battles with police officers outside a mosque about 16km away in the city's old quarters, throwing stones and bricks as they protested against his visit.
Four people including two police officers were injured as police caned the demonstrators, an officer said.
"Allahu akbar (God is the greatest)," the youth shouted as they rushed out of the mosque and tried to breach a police cordon in the street.
"Bush Enemy" read a banner on the wall of the mosque.
Banners in English and Urdu that read, "Bush, the enemy of human rights", were strung over streets.
Hundreds of Communist Party supporters carried red flags as they gathered for a protest march.
BV Raghavulu, a leader of the Communist Party of India (Marxist) said: "We are protesting against George Bush because he is a warmonger. We are demanding the evacuation of American troops from Iraq."
Traffic was sparse in the usually choked streets of Hyderabad's old quarters as markets and businesses shut down in protest.
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.
Protests in Srinagar against controversial caricatures of the Prophet Muhammad turned into an anti-Bush outburst on Friday.
Kashmiris urged Bush to push for
a demilitarised Jammu, Kashmir
Witnesses said hundreds of police and paramilitary personnel were patrolling the streets in Srinagar and elsewhere, Aljazeera's Yusuf Jameel reported from the Kashmir's summer capital.
Some protesters clashed with riot police, who fired teargas to break up the demonstrations.
A statement by the All Party Hurriyat Conference urged Bush to push "India and Pakistan to demilitarise the entire Jammu and Kashmir" in the disputed Himalayan region.
It also urged the US president to resolve the Kashmir situation.
Earlier in India, Bush visited an agriculture university and toured the seed research area where women in saris bent and tended to green patches where peanuts and soybeans had been planted.
The university began collaborating with Cornell University of the US in 2004 to develop Indian agriculture. Security for Bush in the region has been stepped up.
The nuclear deal, which would make US 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 US Congress and, in an indication of possible rough water ahead, a leading Democrat called the pact a "historic failure".
Aljazeera.net's Yusuf Jameel in Srinagar contributed to this report.