In meetings in the capital, New Delhi, Clinton was expected to push for India to find alternative sources of oil on the international market.
Earlier Monday, she told a town hall meeting in the eastern city of Kolkata that there's an adequate supply in the market for India to find other suppliers. Clinton noted India has taken some steps to reduce its imports from Iran but she says the U.S. wants to see more.
"If there weren't an adequate supply ... we would understand, but we believe that there is adequate supply," she said.
India could face U.S. sanctions by the end of June if the Obama administration determines it has not made significant cuts in imports under a law aimed at squeezing Iran's petroleum industry to press the country to prove its nuclear program is peaceful.
India, with a growth rate of about 7 percent, has a nearly insatiable need for oil. About 9 percent of its oil imports are from Iran, though officials say it has reduced its dependency on Iranian oil in recent months,
"We appreciate what has been done and, of course, we want to keep the pressure on Iran," Clinton said.
However, India remains dependent on the imports, and Iran is its second largest oil supplier after Saudi Arabia. With international sanctions making it difficult to find banks willing to handle Iranian oil payments, India and Iran reached an agreement earlier this year that would allow India to pay for about 45 percent the purchases in rupees. Iran would then use the Indian currency to buy goods from India.
Clinton said the U.S. remained focused on putting global pressure on Iran.
"We believe, at this moment in time, the principle threat is a nuclear-armed Iran," she said. "We need India to be part of the international effort."
When asked whether India could get a waiver from the Iran sanctions, Clinton said it was too early to discuss that possibility.
Clinton also met Monday with West Bengal Chief Minister Mamata Banerjee, a key partner of India's ruling coalition who has stymied government efforts to lift restrictions on foreign-owned investments in the country.
Clinton had a long conversation with Banerjee about allowing multi-brand retailers, such as Wal-Mart, enter the market, U.S. officials said after the meeting.
Last year, India's Cabinet had to rescind a decision to open up its market to major foreign retailers after Banerjee balked at the move, saying it would crush small domestic retailers.
Banerjee described the meeting with Clinton as "positive, constructive, creative and concrete," and said they discussed the possibility of increased U.S. investment in everything from tourism to education in West Bengal.
Clinton gave Banerjee a mat emblazoned with a picture of Nobel Prize winning Bengali poet Rabindranath Tagore and a line from one of his songs. Banerjee gave Clinton a scarf and several books, including a translation of Tagore's masterpiece Gitanjali.
Clinton later flew to Delhi, where she was also to press for the renewal of stalled economic reforms. The prime minister's chief economic adviser said last month that no new reform measures were likely before 2014 elections.