President Bush has branded the former Soviet domination of eastern Europe one of "the greatest wrongs of history".
Speaking in Latvia to mark 60 years since the end of WWII in Europe, Mr Bush also acknowledged the US role in the division of Europe after the war.
In Moscow, President Putin stressed Russians had been liberators.
The Baltic states, backed by the US, have demanded Mr Putin issue a new apology for the Soviet occupation. But he says this has already been done.
In an interview with German TV, Mr Putin noted that Soviet-era authorities had issued a resolution in 1989 criticising the 1939 Molotov-Ribbentrop Pact - which handed the previously independent Baltic states to the USSR - so Moscow had no reason to do so again.
Speaking in Riga, Latvia's capital, Mr Bush praised the Baltic nations of Latvia, Estonia and Lithuania - now members of the EU and Nato - for keeping "a long vigil of suffering and hope" during almost 50 years of Soviet occupation.
While the end of World War II brought peace to these countries, it also brought "occupation and communist oppression", Mr Bush said after talks with the presidents of the three countries.
The 1945 Yalta agreement between Britain, Russia and the US, which paved the way for the post-war division of Europe, followed the unjust traditions of pre-war diplomacy, Mr Bush said.
"We will not repeat the mistakes of other generations - appeasing or excusing tyranny, and sacrificing freedom in the vain pursuit of stability," he added.
Russia has protested against Mr Bush's visit to Latvia ahead of his trip to Moscow to attend major commemorations.
Laying a wreath at a Moscow monument to the Soviet Union's 30 million war dead, Mr Putin for his part praised the Soviet war effort, now a source of considerable national pride in modern-day Russia.
Russia sees itself as the main power which helped bring freedom to Europe, defeating the Nazis at an enormous human cost.
The world has never known such heroism," he said.
"Our people not only defended their homeland, they liberated 11 European countries."
Mr Bush has promised to raise the Baltic issue with Mr Putin when he travels to Moscow for Monday's official ceremonies.
He has urged all nations to reconcile the events of the past, and called for democratic elections in Belarus, a state he called Europe's "last dictatorship".
Yet of the three Baltic countries, Latvia alone will be taking part in Moscow's ceremonies.
Estonia and Lithuania are staying away.
The rift between them and Russia has deepened over the refusal to issue a fresh apology.
Interviewed by a French newspaper on Saturday, Mr Putin alleged that the Baltic complaints were being aired to mask a "discriminatory, reprehensible policy" against the Russian-speaking minorities in their countries.
Mr Bush was due to fly to the Netherlands on Saturday afternoon, before leaving for Russia on Sunday.
From Russia, Mr Bush will fly to Georgia - against a backdrop of worsening relations between Tbilisi and Moscow, which has also opposed this part of the US leader's trip.