The Prime Minister discussed the entire spectrum of their bilateral relationship, including ways to boost trade and investment ties with Leuthard, officials said.
PM Modi also discussed various regional and global issues of mutual interest with Doris.
Earlier in the day, External Affairs Minister Sushma Swaraj also called on the President of the Swiss Confederation and discussed various bilateral issues.
“First engagement for an honoured guest. EAM @SushmaSwaraj called on President Leuthard and discussed wide-ranging issues of mutual interest,” External Affairs Ministry Spokesperson Raveesh Kumar tweeted.
Leuthard, who is on a three-day visit to India, was also given a ceremonial welcome at the Rashtrapati Bhavan.
The Swiss president is accompanied by senior government officials and a large business delegation of leading Swiss companies.
It was only the fourth visit to India by a Swiss president. Earlier in 1998, 2003 and 2007 Swiss presidents visited India.
Notably, PM Modi visited Switzerland in June last year. During the visit, the country announced its support to India’s membership of the Nuclear Suppliers Group.
The two countries had also resolved to strengthen cooperation in combating tax evasion and black money.
(With PTI inputs)