She said this on Tuesday during a phone conversation with Prime Minister Narendra Modi who called her to congratulate on the assumption of new responsibility.
"Modi recalled his memorable visit to Britain last November and affirmed India's commitment to further strengthen the strategic partnership between both countries," External Affairs Ministry spokesperson Vikas Swarup said.
Modi also appreciated Britain's consistent support to India in various global fora, Swarup said.
Theresa May succeeded David Cameron, who hosted Modi last year, after the former Prime Minister resigned following Britain's sensational exit from the EU on June 24.
In a referendum last month about 52 per cent Britons voted to exit from the EU against 48 per cent who opted to stay.
Following the result, the Indian High Commission in London held a meeting with representatives of various sectors of Indian businesses in Britain to understand their reaction to the referendum's outcome.
There are over 1.5 million people of Indian-origin in Britain, including around 20,000 students.
India has asserted that it would continue to boost its good ties with both Britain and the EU after the country's exit from the 28-member bloc.
According to Swarup, in Tuesday's conversation, May thanked Modi and said she looked forward to working closely with him "for developing stronger bilateral ties and enhancing cooperation in tackling pressing global challenges".
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