The G-8 summit of the world's most industrialized nations is scheduled to be held in Scotland next month.
Going into the meeting, Putin said Moscow was counting on Britain's help when Russia takes over the chairmanship of the G-8.
"We hope that Great Britain will give us its support when we chair the G-8 next year. We will be glad to use your experience and your advice," Putin said.
Blair said Britain, which currently chairs the G-8, was interested in working as closely as possible with Russia.
The two leaders were scheduled to give a press conference after their meeting ends later today.
Blair arrived in Russia yesterday as part of his official visits to G-8 countries ahead of the summit in Scotland.
From Moscow, Blair is due to travel on to Berlin for talks with German Chancellor Gerhard Schroeder. Those talks are expected to focus on the G-8 summit and the crisis in the European Union following the rejection of the EU constitution by French and Dutch voters.
Blair is due to hold consultations in Paris and Luxembourg on 14 June ahead of the EU leaders' summit on 16-17 June in Brussels.
(AFP/dpa/Reuters)More news and features on Russia