Indian External Affairs Minister S.M. Krishna is in talks with top U.S. officials in Washington as part of a broad-based dialogue session.
Clinton during talks with her Indian counterpart said both sides shared common concerns regarding nuclear issues and counter-terrorism.
"Both India and the United States have seen our cities and our citizens targeted by violent extremists and we share concerns about the continuing threat of terrorism and we share concerns about the dangers of nuclear proliferation," she said.
Nuclear-armed foes India and Pakistan suffered a breakdown in already-tense relations following the November 2008 attacks on Mumbai from Lashkar-e-Toiba, a Pakistani-based guerrilla organization.
On the nuclear issue, Clinton said she welcomed a nuclear processing agreement with India, adding climate negotiations showed bilateral ties extended beyond defense issue.
Krishna, for his part, said his country was looking forward to a U.S. partnership in the spirit of international peace.
"We have an increasing and well-justified stake in a stable international order," he said. "We are committed to working with the international community to find solutions to the pressing global challenges of the day."
Clinton added that Washington was "committed" to considering India for the U.N. Security Council.