These are not issues that resonate greatly with the Russian public, but Blair will not anticipate much in the way of Russian opposition. Indeed, Moscow has already joined the other members of the G-8 in agreeing to the deal on debt relief. Finance Minister Aleksei Kudrin explained that in any case Russia had held little hope that the debts owed it would ever be repaid.
And by signing up to the Kyoto Protocol on greenhouse gas emissions in February this year, Russia has already signaled some support at least for the need for action on climate change.
Little wonder then that the diplomatic niceties preceding the meeting between Blair and Putin sounded even more bland than usual. Britain wants Russian support on these issues at the G-8 summit in Scotland in July and Moscow can see no reason not to give it. At least not for the moment. Putin did hint though that he expects something in return.
"We hope that Great Britain will give us its support when we chair the G-8 next year," Putin said. "We will be glad to use your experience and advice."
The Russian leader might also have had in mind that Britain is due to assume the six-month rotating presidency of the European Union. There are some in Europe who believe it is time for Brussels to be more critical of Russia's record on human rights and what some see as its retreat from democracy.
Britain has itself voiced the occasional criticism -- albeit softly and rarely in public. The meeting in Moscow was no exception. Tony Blair gave no grounds for offence.
"We also had a very interesting talk about the present state of Russia and how it will develop in the future, which I found -- um, fascinating," Blair said.
Blair told the Russian leader that Britain intended to devote a significant part of its EU presidency to developing Brussels' relations with Moscow. Putin will want to persuade him to hold the more vociferous critics of his policies in check. Support for Britain -- and at no critical cost to Russia's interests -- at the G-8 summit might make his case more persuasive.
After Moscow, though, the going for Blair gets more tough. His whirlwind tour takes him through Germany, France, and Luxembourg, where the current preoccupation is more with the future of Europe and a rapidly deepening row between London and Paris over the question of Britain's budget rebate than the need for the world to cut back its greenhouse emissions.
Blair will want to try and focus minds on the G-8 summit in July but with the EU leaders to meet in Brussels for a critical summit on 16 June his chances look slim. On 12 June, British Foreign Secretary Jack Straw described as "deluded" the demands by French President Jacques Chirac for Britain to back down on the issue of the rebate. When Blair leaves Moscow, he will be heading into a maelstrom.