NEW DELHI—Defense Secretary Jim Mattis arrived in India on Monday on a trip to reinforce a budding U.S.-India defense partnership and to look for ways to work with India to expand ties in Afghanistan and counter Chinese influence in the region.

Mr. Mattis, the first cabinet secretary to visit India in the Trump administration, described India as a “major defense partner,” the result of progress made in recent years that strengthened the nations’ common security interests.

The closer relations are important to the Trump administration’s Afghanistan-Pakistan strategy, as well as to U.S. policy in Asia, where the U.S. is attempting to counter a more aggressive China in the South China Sea.

“This is a historic opportunity for our two democracies, a time of strategic convergence,” Mr. Mattis told reporters on a military jet en route to New Delhi on Sunday, adding that “steady engagement” would be fitting watchwords for the path ahead for the two countries.

A series of talks in New Delhi, which include meetings with Indian Prime Minister Narendra Modi and the new minister of defense, Nirmala Sitharaman, follows Mr. Modi’s June visit to Washington, during which Mr. Trump called India “a true friend.”