During the meeting, their first ever, Putin congratulated May on becoming the British Prime Minister, and said he hopes the two countries can take bilateral relations to a higher level, Xinhua news agency reported.
"We certainly have much to do -- both in the political and economic spheres," he added.
Relations between Moscow and London have been strained in recent years due to their different stances over the Ukraine and Syria crises.
May, for her part, recognised the existence of "some differences as well as some complex and serious issues of common concerns" between the two countries, calling for a "frank and open relationship and dialogue".
Putin and May also touched on such issues as counterterrorism, the Syria crisis, aviation safety and drug-trafficking, Russian Economic Development Minister Alexei Ulyukayev said after the meeting.
The Russian and British leaders are both in the Chinese city of Hangzhou for the 11th summit of the Group of 20 major economies.
