Clinton, said New Delhi should exercise political influence to match its fast-growing economic muscle.
"This is not a time when any of us can afford to look inward at the expense of looking outward. This is a time to seize the opportunities of the 21st century and it is a time to lead," Clinton said.
U.S. officials billed Clinton's speech as a major address to outline Washington's vision for the U.S.-India partnership in the coming century.
U.S. President Barack Obama, on a visit to India last November, publicly backed New Delhi's bid for a permanent seat on the U.N. Security Council and U.S. officials say they are looking to the world's largest democracy to become a more visible partner in facing global challenges.
"India, China and the United States will have to coordinate our efforts."
India, and the United States are looking with concern at China's increasingly assertive role, not just in its backyard but also across the world where it can now combine economic and political might.
India and the United States, once on the opposite side of the Cold War divide, have boosted ties over the past decade, as New Delhi seeks a greater global role but at the same time the country's very DNA is traditionally to avoid being seen siding with one power or the other.
The United States, especially in light of challenges in Afghanistan and Pakistan, wants India to be an all-weather ally, but a large part of the political elite in India still regard Washington with suspicion, partly because of its reluctance to take its side on nuclear-armed rival Pakistan.
Clinton said India should do more to support both political and economic progress in Afghanistan, where the Obama administration has begun drawing down troops.
India is Afghanistan's biggest regional aid donor, having pledged $2 billion to help build roads and power lines in an attempt to secure influence in a country it considers crucial to its security.
"We all need to be working together."
She said India could work with Pakistan and its other neighbours to "adopt new rules for the 21st Century" to bring down trade barriers and encourage regional projects such as a proposed natural gas pipeline stretching from Turkmenistan to India.