Both the leaders held discussions on the sidelines of the G20 summit on "building opportunities" after the UK voted to leave the EU -- the world's single largest market.
"Building opportunities with the United Kingdom. PM @narendramodi meets PM @theresa_may for their first bilateral," External Affairs Ministry spokesperson Vikas Swarup tweeted.
May was sworn in as Britain's prime minister on July 13, succeeding David Cameron who resigned after the country voted in favour of exiting the EU.
May, 59, is UK's second woman prime minister after Margaret Thatcher, also known as Iron Lady, with whom May is often compared.
Modi had congratulated May on her assumption of new responsibility on July 27 and had affirmed India's commitment to further strengthen the strategic bilateral partnership.
Thanking Modi, May had during the telephonic conversation said she looked forward to work closely with India to develop stronger ties and enhance cooperation.
Earlier in the day, Modi said fighting corruption, blackmoney and tax-evasion were central to effective financial governance.
He also said, "We need to act to eliminiate safe havens for economic offenders, track down and unconditionally extradite money launderers."
Modi held separate "pull-aside" meetings with French President Francois Hollande and Turkish President Recep Tayyip Erdogan on the sidelines of the G20 summit on Monday.
"Strengthening the Strategic Partnership with France. PM @narendramodi has a quick pull aside with President Hollande," External Affairs Ministry spokesperson Vikas Swarup tweeted.
Modi was accompanied by National Security Advisor Ajit Doval and foreign secretary S Jaishankar during the brief meeting with the French President.
Earlier on Sunday, Hollande, in a Facebook post, said "France's role is to contribute to regulating the planet".
"Our country refuses a globalization without rules, where social models are pit against each other and dragged downward, where inequalities grow and intellectual property rights, and therefore cultural diversity, are threatened," Hollande said.
Hollande has lauded the US and China for approving the Paris climate deal.
Meanwhile, Modi also met with Turkish President Recep Tayyip Erdogan for the first time after a failed coup attempt in Turkey and held discussions on renewing bilateral ties.
"Renewing ties with Turkey. PM @narendramodi meets Turkish President @RT_Erdogan in another pull aside," Swarup said in another tweet.
In July, a coup was attempted in Turkey against the Erdogan government. The attempt was carried out by a faction within the Turkish Armed Forces.
Modi earlier said fighting corruption, blackmoney and tax-evasion were central to effective financial governance.
He also said, "we need to act to eliminate safe havens for economic offenders, track down and unconditionally extradite money launderers".
Photograph: Vikas Swarup/MEA/Twitter