"We are committed to work with the government of Mauritius to jointly fight piracy and enhance security in the Indian Ocean through mutually agreed measures," Patil said while speaking to reporters on-board the special Air India aircraft.
Patil also said India "will help the Mauritian government in setting up an anti-terrorism cell".
Patil, upon her arrival, was accorded a red carpet welcome and was received by Prime Minister of Mauritius Naveen Ramgoolam, who was accompanied by his wife.
She was then presented with a guard-of-honour and a 21 gun-salute as the national anthem was played.
"The India and Mauritius partnership today is wide-ranging and multi-faceted and its depth and diversity indicates that it is a mutually beneficial relationship. Our common commitment to democratic ideals and pluralistic society anchors our close ties. We aim to further enhance the level of our engagement to newer heights.
"My discussions with the leadership of Mauritius will cover a wide range of bilateral, regional and international issues of mutual interest. I hope that the exchange of views at these meetings will provide a greater momentum and thrust to the process of consolidation and development of our partnership in all spheres," she said.
"Mauritius has extended support to India on global issues of crucial importance to us. It has consistently supported India's candidature for a permanent membership in an expanded United Nations Security Council. It has been unequivocal in its condemnation of international terrorism," Patil said.
During Patil's stay in Mauritius, the country's Opposition Leader Paul Raymond Berenger, Chief Justice Justice Bernard Sik Yuen, and Speaker of the National Assembly Rajkeswur Purryag will call on her.
A high-level business delegation consisting of 57 people from India will also be in Mauritius during the President's visit.
The President will also visit heritage sites such as the Aapravasi Ghat and the Le Mourne and address an India-Mauritius Business Meet.
Patil said she was "looking forward to her visit to the country as an opportunity to re-affirm our unique relationship and to further strengthen the framework of co-operation." During the visit, the President will also be conferred Honorary Degree of Doctor of Civil Law by the Mauritius University.