The Pentagon chief arrived today for a 48-hour trip -- the first to India by any member of President Donald Trump's cabinet.
"This is a historic opportunity for our two democracies at a time of strategic convergence," Mr Mattis told reporters on his flight. He is to meet Prime Minister Narendra Modi and Defence Minister Nirmala Sitharaman in Delhi.
The trip comes weeks after Mr Trump unveiled a new Afghanistan strategy and urged India to increase assistance to the war-torn nation's economy.
The US president also chided Pakistan for offering safe haven to "agents of chaos".
"Any nation that is living by the traditional rules of non-interference in other states in today's age of anti-terrorism, they will not find this relationship in any way adversarial," he said.
India has long vied with Pakistan for influence in Afghanistan, building dams, roads and a new parliament in the troubled country. Last year it offered some $1 billion in aid.
Mr Trump's new Afghan strategy includes the deployment of more than 3,000 additional US troops.
In 2016, the United States designated India a "Major Defence Partner" with the aim of improving military cooperation, increasing information-sharing and cutting red tape to ease defence deals.
Mr Mattis's predecessor Ash Carter pushed hard for stronger defence ties and the Trump administration has the same aim.
Mr Trump has praised India for contributing to regional stability and for buying US military equipment.
India is contemplating buying Lockheed Martin's F-16 Block 70 aircraft in a deal potentially worth $15 billion.
The US firm has offered the most upgraded version of the jet fighter to India, the world's largest weapons importer.
It is competing with Swedish defence giant Saab, whose Gripen E made its maiden flight in June.
A drone deal for the Indian Navy will also likely be up for discussion, a source familiar with the negotiations told AFP.
"Since Chinese assets have started to dominate the Indian Ocean region, the Trump administration is keen on fast-tracking the acquisition of the drones," the source said.
Many commentators have said US-India cooperation could act as a counterweight to an increasingly assertive China, which has been developing its military capabilities.