Clinton placed a bouquet of white gladiolas at the tomb and joined several nuns in singing the hymn, "Make me a channel of your peace," said Sister Nirmala, who succeeded Mother Teresa as head of the Missionaries of Charity.
"I promised my wife I would come here," Clinton told reporters outside the orphanage. Clinton said that when his wife, Sen. Hillary Clinton, had returned to Washington after the funeral of Mother Teresa, she had told him, "You must go to Calcutta."
In the orphanage, Clinton danced and sang with some of the 300 children and autographed their paintings of him. He also held some of the babies.
Earlier, shouts of "Clinton, Clinton" broke out from a 1,000-strong crowd held back by police on the other side of a wide avenue as the former president arrived at Mother House, towering over Sister Nirmala by his side. He said he didn't mind the 90-degree temperature. "It's like Florida," he said.
"Mr. Clinton is a very good man with a very good heart," Sister Nirmala was quoted as saying by The Press Trust of India.
Roads and shops were closed, the street divider was painted green, and lime was sprinkled to cut down on the stench of garbage.
Clinton arrived from Bombay aboard a chartered Indian Airlines jet with 40 people from the American India Foundation, which sponsored his seven-day Indian visit to raise funds for victims of the Jan. 26 earthquake in Gujarat state.
Clinton met with volunteer organizations before flying to New Delhi.
In the Indian capital, Prime Minister Atal Bihari Vajpayee canceled a dinner planned for Clinton because of the death Friday of a former deputy prime minister, Devi Lal. But Vajpayee and Clinton later held an informal talk at the prime minister's residence.
On Sunday, Clinton heads to Rampur, in Uttar Pradesh state, to dedicate a women's polytechnic school in the name of his wife. He was to spend Sunday evening and the next day in the ancient city of Jaipur, capital of the desert state of Rajasthan, and tour a former palace.
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