President Bush continued to focus on how this latest round of violence began, laying the blame clearly with Hezbollah for launching rockets into northern Israel and kidnapping two Israeli soldiers.
"The best way to stop the violence is for Hezbollah to lay down its arms and to stop attacking, and therefore I call upon Syria to exert influence over Hezbollah," said Mr. Bush.
President Bush and President Putin met privately ahead of the start of a summit of the Group of Eight industrialized nations outside St. Petersburg.
Mr. Bush says Islamic militants started the fighting to disrupt what he says was progress by Israeli Prime Minister Ehud Olmert to pursue a two-state solution to the Israeli/Palestinian conflict.
"As the vision was progressing, certain terrorist elements began to act to stop the advance of democracy," he said. "The militant wing of Hamas made decisions to attack and to capture. Hezbollah has made decision to stop the advance of a two-state solution."
President Bush has continued to back Israel's right to defend itself against such attacks.
While denouncing the violence on both sides, President Putin questioned the appropriateness of Israel's response which has included bombing Beirut's airport and the main road to Syria.
The Russian leader said all bloodshed should stop as soon as possible.
"I agree with the premise that it is absolutely unacceptable to reach this or that goal, including political goals, through the use of force, through abductions, through carrying out strikes against an independent state from the territory of another state. This is all true, and in this context, we consider Israel's concerns to be justified," said Mr. Putin. "At the same time, we work the assumption that the use of force should be balanced."
President Putin says he and President Bush will take every necessary action to try and find common ground between the combatants to reach a conclusion that not only stops the fighting but also creates an enabling environment for Israel within secure borders.
President Putin had hoped to focus this G8 summit on energy security and fighting infectious disease, but continuing Middle East violence will likely dominate these talks.