Clinton was paying the first visit by a top US official to the eastern metropolis Kolkata and will then meet in New Delhi with Prime Minister Manmohan Singh, amid concern that the growing US-India partnership has been drifting.
The world's two largest democracies have rapidly expanded ties since overcoming mutual mistrust during the Cold War, but have been going through one of their most open spats in years over US efforts to pressure Iran.
A US law will slap sanctions starting June 28 on banks from countries that keep buying oil from Iran, amid charges by Israel and some Western officials that the regime is building a nuclear bomb.
India is highly dependent on oil imports and since its independence has strongly resented any moves it sees as foreign diktats.
Indian companies have been quietly reducing Iranian oil, although a major Iranian trade delegation is visiting New Delhi at the same time as Clinton.
A US official said India had made "good progress" but Clinton would seek further assurances as Washington determines whether to exempt India from the sanctions. It has already exempted European Union nations and Japan.
Clinton is expected also to stress areas of growing convergence with India. US officials were pleasantly surprised when India, in response to domestic pressure, backed a US-led UN resolution pushing Sri Lanka on human rights.
India has also been repairing ties with historic enemy Pakistan, removing a headache for the United States whose own relations with Islamabad have been in crisis since US forces killed Osama bin Laden a year ago.
Clinton said she will speak at a forum in Kolkata about the economy and about investment opportunities in its state of West Bengal, which is strategically close to booming East Asia but has had less dramatic growth than some parts of India.
"I will have a chance to meet with a cross-section of the citizens from here in Kolkata, including a lot of young people, and talk about the future of this country and our relationship," Clinton told US consulate employees.
On Sunday, Clinton sought to draw attention to sex trafficking in India, where forced prostitution of women and girls is one of the largest illicit businesses.
Clinton appeared visibly moved as she watched a dance by former victims of sex trafficking, who recounted their plight in a synchronised performance designed as a form of therapy by the local group Kolkata Sanved.
Clinton called the recital "mesmerising" and thanked each of the six dancers, telling them she was proud of them. She was shown quilts which former trafficking victims sew as a way to give them new livelihoods.
"What you're doing is so important to try to not only help yourselves but to help other young girls," Clinton said.
An enthusiastic girl showed off a karate kick she had mastered -- nearly clobbering some of the US entourage -- and handed to Clinton two T-shirts and bracelets emblazoned with the slogan, "Cool men don't buy sex."
The United States last year took India off a watchlist of countries judged not to be doing enough on trafficking, crediting the government with taking the issue more seriously by setting up special units to fight the scourge.
Some anti-trafficking advocates in the United States criticised the move, saying India had not yet shown results and accusing the State Department of caring more about preserving relations with New Delhi.
Clinton will meet Monday with West Bengal's chief minister, Mamata Banerjee, to show support for a fellow woman leader.
Banerjee last year ended nearly 35 years of communist rule in the state, where the US consulate lies on a street that local leaders provocatively renamed after Ho Chi Minh.
Clinton is expected to nudge Banerjee to support opening India's retail sector to foreign giants such as Walmart after the West Bengal leader's party scuttled the move in parliament.
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