The focus of this visit is to be completion of a historic nuclear cooperation deal.
President Bush and Indian Prime Minister Manmohan Singh reached an agreement in principle last July to provide help for India's civilian nuclear power industry, while at the same time putting the program under international safeguards.
Negotiators say the final deal is almost complete, but acknowledge the most difficult issue remains: how to provide guarantees that technology provided to India's nuclear power program will not be diverted to develop nuclear arms.
India is trying to come up with a formula to separate its civilian and military nuclear programs, which have long been intertwined. Both sides say it can be done, but President Bush acknowledges it is not easy.
"It is a difficult issue for the Indian government; it is a difficult issue for the American government," he said. "And so we will continue to dialogue and work and hopefully we can reach an agreement. If not, we will continue work until we do."
Mr. Bush says the agreement is important, but stresses there is much more to the Indian-American relationship than this one deal between Washington and New Delhi.
"Our relationship with India is broader than our discussions about energy," he said. "Ours is a strategic relationship. It is a relationship that's got strong ties because of our economies and our military, [and] our desire to help democracies such as Afghanistan."
New Delhi was supposed to be the first stop on the president's South Asia tour. Instead, he made a detour to Afghanistan.
"Mr. President, welcome to Afghanistan!" said Afghan President Hamid Karzai. He hosted President Bush for a working lunch in Kabul - their first meeting on Afghan soil. The surprise visit lasted about five hours.
In addition to his talks with Mr. Karzai, President Bush participated in ceremonies marking the official opening of the U.S. embassy, and he spent time with American and coalition troops at the Bagram military base.