Netherlands Prime Minister Mark Rutte also called on Modi and congratulated him on his victory.
Putin also extended an invitation to Modi to visit Russian Federation in near future.
In his message, he said he is looking forward to meet him at the BRICS Summit in Brazil and expressed hope that they will be able to discuss bilateral cooperation.
Emphasising that relations between the two countries are multi-dimensional, he said that he looks forward to the bilateral summit to be held in India later in the year.
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Modi thanked Putin for his wishes and recalled his visit to Russia and meeting the President. He said India values friendship and support of Russian Federation and its people.
Congratulating Modi, Rousseff said her country will provide great support in further strengthening of bilateral relations with India.
Looking forward to receive Modi at the BRICS Summit in Fortaleza in northeastern Brazil, she said that the event will provide an excellent opportunity to share and exchange views.
Rutte said the Netherlands' connection with India is 400 years old and had its roots in Surat. The Dutch prime minister said that he has been following the general elections and popularity of Modi.
He said he is looking forward to meet Modi at the earliest and expressed hope that under his leadership cooperation between Netherlands and India will grow.