Mrs Clinton also held talks with the leader of the opposition, Lal Krishna Advani.
India's relations with neighbouring Pakistan were also expected to feature prominently in discussions.
Our correspondent says that publicly Mrs Clinton has insisted that what Pakistan and India do is completely up to them.
But he says everyone in Delhi is clear it was pressure from Washington that pushed the countries to hold talks in Egypt last week.
Pakistan-India relations dominated Mrs Clinton's visit to Mumbai on Saturday, in the wake of attacks on the city last November that left more than 170 people dead.
Clinton: "I have seen a real commitment on the part of Pakistan"
On Sunday, talks in Delhi focused on climate change, which remains a sensitive subject for developing countries such as India and China, which have so far refused to commit to carbon emissions cuts in a new treaty.
Mrs Clinton also sought to assure India the US would not try to impose conditions that might affect India's economic growth.
But Indian Environment Minister Jairam Ramesh said his government could not accept targets that would limit economic growth.
India argues the US must do more as it has been historically to blame for the emissions.
Mrs Clinton later told reporters she was optimistic a deal on climate change could be reached.
The key date for climate change is December - when a summit in Copenhagen will look to forge a new international treaty that will replace the Kyoto Protocol, which expires in 2012.
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