The two countries are negotiating the first tranche of a trade deal, which New Delhi hopes to secure within the 90-day pause on tariffs announced by US President Donald Trump this month.
Vance’s four-day visit comes two months after Modi held talks at the White House with Trump, who unveiled 26 percent tariffs on India.
A red carpet welcome with an honour guard and troupes of folk dancers greeted Vance after he stepped out into the sweltering sunshine of New Delhi on Monday morning, the start of a four-day tour that will include trips to the historic fort city of Jaipur and the Taj Mahal.
“Ad-Vance-ing” US-India ties, broadcaster NDTV headlined its stories.
Modi welcomed Vance to his residence on Monday evening, giving his US visitor a bear hug, photographs released by the Indian government showed.
A spokesperson for Vance said they would first hold talks before a family dinner hosted by Modi.
Vance’s visit comes during an escalating trade war between the United States and China. India’s neighbour and rival faces US levies of up to 145 percent on many products.
Beijing has responded with duties of 125 percent on US goods. New Delhi has reacted cautiously so far.
India’s Department of Commerce said after the tariffs were announced it was “carefully examining the implications”, adding it was “also studying the opportunities that may arise.”
Vance and Modi were expected to “review the progress” in relations, according to India’s foreign ministry.
“We are very positive that the visit will give a further boost to our bilateral ties,” India’s foreign ministry spokesperson Randhir Jaiswal told reporters last week.
The US vice president is accompanied by his wife Usha, the daughter of Indian immigrants.
Together with their three children, dressed in traditional flowing Indian attire, they visited the Hindu Akshardham Temple in New Delhi.
Modi said during his visit to Washington that the world’s largest and fifth-largest economies would work on a “mutually beneficial trade agreement.”
The United States is a crucial market for India’s information technology and services sectors but Washington in turn has made billions of dollars in new military hardware sales to New Delhi in recent years.
Trump could visit India later this year for a summit of heads of state from the Quad.
Vance, 40, a devout Catholic convert, arrived in New Delhi a day after meeting Pope Francis in the Vatican.
The vice president said his “heart goes out to the millions of Christians all over the world who loved him,” after the Vatican announced the death of the pope on Monday. (AFP)