Modi's telephone call was among a handful received by the British Prime Minister today, during which both leaders agreed to continue to cooperate closely on counter-terrorism.
"Prime Minister Narendra Modi conveyed his country's deepest condolences and said India's prayers were with all of those affected," Downing Street said in a statement.
It said Prime Minister Modi congratulated the people of Manchester on their courage, patience and spirit.
India and the UK have a Defence and International Security Partnership dating back to 2015, which involves working on closer cooperation on countering terrorism, radicalisation, violent extremism and cyber security.
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May and Modi had reiterated the partnership during the former's visit to India in November 2016.
The other calls taken by May following Monday night's terrorist attack in Manchester included German Chancellor Angela Merkel, King Salman of Saudi Arabia and Swedish Prime Minister Stefan Lofven.
"Chancellor Merkel called to offer Germany's condolences and said Germany stands with the UK against terrorism. They agreed the deliberate targeting of children was despicable and that the people of Manchester had shown great spirit in coming together in the wake of the attack," Downing Street said.
Modi's conversation with May came as he prepares for his visit to Germany next week, during which greater collaboration on counter-terrorism is expected to be among the issues discussed during his bilateral talks with Merkel.