"On reaching Davos, held talks with the President of the Swiss Confederation, Mr @alain_berset. We reviewed the scope of our bilateral cooperation and discussed ways to deepen it even further," Modi said in a tweet.
Berset said the discussions marked the meeting of the biggest and the oldest democracies in the world.
Thanking Modi, the Swiss President said he would continue to strengthen "our relations" with India.
"First engagement in snowing #Davos, PM @narendramodi met with Swiss President @alain_berset. Two leaders had productive discussions on steps to further deepen our bilateral cooperation built upon our shared values of democracy and diversity. #IndiaMeansBusiness," an external affairs ministry spokesperson said in a tweet.
Negotiations on EFTA (European Free Trade Association) trade pact and the bilateral investment protection agreement were also discussed, among various business and trade matters, they added.
Modi, who arrived at the ski-resort today, would be delivering the keynote address at the summit's plenary session tomorrow.