Leaders from eight countries are expected to discuss a range of economic and political issues at the three-day summit, which begins Saturday.
Before the serious business got under way, the president and his Russian counterpart had time to get reacquainted.
Mr. Bush drove himself and the first lady, in a golf cart, to the cottage where the dinner was held. Shortly after arriving, he admired an old car parked nearby that Putin said was his first.
When someone asked Mr. Bush about his first car, he replied, "My first car was a Triumph." Putin joked, "Bicycle, bicycle." A Triumph is a classic British car.
As the group left to eat dinner, Mr. Bush jokingly told reporters, "Go find some Russian vodka and relax."
The two presidents are trying to put a new shine on U.S-Russian relations, which have grown strained over such issues as Russian backsliding on democracy, Iran and North Korea — and now the Middle East.
The presidents are also trying to conclude a new trade deal during this visit, CBS News Moscow bureau chief Beth Knobel reports, but it's not clear if anything of substance will be accomplished.
Meanwhile, the Mideast crisis threatened to dash Mr. Bush's hopes to see the G-8 summit produce a united stand against Iran's nuclear ambitions and North Korea's long-range missile test.
While on Air Force One, Bush called three Arab moderates, King Abdullah of Jordan, President Hosni Mubarak of Egypt and Fouad Siniora, the new prime minister of Lebanon. He thanked them for distancing themselves from Hezbollah, but made it very clear that he would not tell Israel how to conduct its military operations, reports CBS News chief White House correspondent Jim Axelrod.
White House spokesman Tony Snow said it seemed inevitable that the G-8 members would issue some kind of a statement on the Mideast situation, but it was unclear what it would say. Secretary of State Condoleezza Rice said a three-person team sent by the United Nations to the region should get a chance to try to defuse the crisis.
Several drafts concerning violence in the Middle East were already on the table. "With the pace of events, they're going to have to redraft them," Snow said.
"It is important that everybody talk with one voice," Snow said.
In St. Petersburg, Mr. Bush's first stop was a monument honoring those who defended Leningrad, the Soviet name for the city during the 900-day World War II siege. More than half a million people died, most of hunger. Mr. Bush and his wife paused there for a long moment of silence.
In what amounted to a gentle statement about democratic backsliding under Putin's leadership, Mr. Bush went from there to sit down with 17 representatives from civil society groups whom he called "young, vibrant Russian activists who loved their country" but who also are concerned about human conditions there. The president said he planned to convey some of their worries directly to Putin.
"I assured them the United States of America cares about the form of government in Russia," Mr. Bush told reporters afterward. "I hope I was encouraging for them. It was instructive to me."
Mr. Bush and Putin meet as U.S. and Russian negotiators try to conclude a deal to let Russia join the World Trade Organization. Russia hoped to have the presidents announce it as early as Saturday.
But while officials reached a breakthrough in banking, officials said U.S. Trade Representative Susan Schwab and Russian Economics Minister German Gref continued working Friday on a number of other sticking points.
"There is no resolution at this point," said Sean Spicer, Schwab's spokesman.