The two leaders also deliberated on regional and global issues of mutual interest.
Earlier in the day, External Affairs Minister Sushma Swaraj called on the Swiss president 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, was also given a ceremonial welcome at the Rashtrapati Bhavan.
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Swiss presidents have visited India on three occasions earlier -- in 1998, 2003 and 2007.
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.
Modi had then said that combating the menace of black money and tax evasion was "shared priority" for both the countries.