Leuthard, whose visit to India also marks start of the 70th anniversary celebrations for the Treaty of Friendship of 1948 between the two countries, also emphasised the need for a bilateral investment protection agreement.
In a statement, her office said the discussion topics during her talks with Prime Minister Narendra Modi included common concerns regarding climate change.
"The situation in South Asia, efforts to combat terrorism, issues surrounding migration and the political and economic situation in Europe were also addressed," the statement said.
The official talks focused on relations between Switzerland and India, particularly the ongoing negotiations on a free trade agreement between the European Free Trade Association (of which Switzerland is a member along with Iceland, Liechtenstein and Norway) and India.
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"Both sides are aware that the potential in economic relations is not yet being fully exploited. They therefore reiterated their commitment to bringing the negotiations to a conclusion.
"President Leuthard stressed that Switzerland was seeking pragmatic solutions. She also emphasised the need for a bilateral investment protection agreement. Good investment protection is important to promote economic relations," the Swiss government said.
The talks also covered financial and fiscal policy.
Noting that international cooperation on combating tax evasion and tax fraud has improved markedly in recent years, the Swiss government said there was a discussion following on from the joint declaration of November 2016 on the introduction of the mutual automatic exchange of information in tax matters with India.
The official talks were further attended by State Secretary Marie-Gabrielle Ineichen-Fleisch, the director of the State Secretariat for Economic Affairs (SECO), State Secretary Joerg Gasser, director of the State Secretariat for International Financial Matters (SIF).
At the start of her visit to India, President Leuthard was received by President Ram Nath Kovind and Prime Minister Modi, after which she laid a wreath at the Mahatma Gandhi memorial at Raj Ghat.
Later, she was to attend a state banquet hosted by President Kovind and meet a number of government ministers during which she will discuss energy, transport, environmental, financial and trade issues.
The focus of her visit tomorrow will be the Treaty of Friendship of 1948 in which Switzerland and India assured each other of 'perpetual peace and unalterable friendship'.
Leuthard will also attend a business event tomorrow on digitalisation with Union Commerce Minister Nirmala Sitharaman.
She is also expected to attend a gathering with students on the topic of energy policy and climate change, and pay a visit to the Hope Project, a social project on education, health education and the advancement of women in Hazrat Nizamuddin Basti in Delhi.