Tillerson arrived from Pakistan, India’s arch-rival, where he was given a low-key reception after US complaints about Islamabad backing Taliban militants on its soil.
In New Delhi Tillerson was to hold talks with Prime Minister Narendra Modi and Foreign Minister Sushma Swaraj. He started the day by meeting national security adviser Ajit Doval.
Tillerson also laid a wreath at a memorial to India’s independence movement leader Mahatma Gandhi, removing his shoes to approach a pillar marking the spot where Gandhi was shot dead on January 30, 1948.
Support for efforts to bolster the Afghan government, China’s influence and other Asian security issues were expected to dominate talks in New Delhi, officials said.
Last week Tillerson called for deeper cooperation with India in the face of growing Chinese influence in Asia and said Washington wanted to promote a “free and open” region led by prosperous democracies.
He also said Beijing sometimes flouted international conventions, citing the South China Sea dispute as an example.
India welcomed the comments, saying they “highlighted our shared commitment to a rule-based international order”.
In Pakistan Tillerson met Prime Minister Shahid Khaqan Abbasi, military chief General Qamar Javed Bajwa and other top officials.
“Tillerson reiterated President Trump’s message that Pakistan must increase its efforts to eradicate militants and terrorists operating within the country,” a statement from the US embassy said Tuesday.
But he also expressed his appreciation to Pakistan for the sacrifices it has made in fighting militancy and for its help in securing the release of a US-Canadian family held captive by the Taliban for five years.