After attending a memorial service in The Netherlands, President Bush arrived in Moscow on Sunday for private talks with Mr Putin.
The two leaders appeared relaxed during Sunday’s meeting, despite recent comments from Mr Bush about Russia’s post-war legacy in Europe.
President Bush hailed Russia’s “bravery and sacrifice” in defeating Nazism, and said he was looking forward to Monday’s ceremonies.
“It is a moment where the world will recognise the great bravery and sacrifice the Russian people made in the defeat of Nazism,” he said during a photo opportunity with the Russian leader.
“The people of Russia suffered incredible hardship and yet the Russian spirit never died down,” Mr Bush said.
His praise was in contrast to comments made during a visit to the former Soviet republic of Latvia two days earlier, in which Mr Bush described the Soviet occupation of Eastern Europe after the defeat of Nazism as was one of “the greatest wrongs of history”.
Moscow has rebuffed calls from Washington for an apology for the Soviet occupation of Estonia, Latvia and Lithuania.
But the US Secretary of State Condoleezza Rice, who is travelling with the president, downplayed any tension between Moscow and Washington.
She said the two presidents would not linger on the past, but would discuss international issues including “the continued march of democracy in Europe and also in Russia”, and added Mr Bush would not be “lecturing” the Russian leader on democracy.
Relations between the two sides have soured recently amid US unhappiness with Russian missile sales to Syria and Washington’s push for democracy along Russia’s borders.
Moscow has not disguised its unhappiness that Mr Bush’s trip to Russia was preceded by visits to two former Soviet republics, Latvia and Georgia.