Though Russia is Syria’s principal arms supplier, Mr. Putin warned the others against United States plans to begin sending some light arms and ammunition to Syrian rebels; even before Mr. Obama’s decision, France and Britain supported an end to a European embargo on arms transfers to the opposition.

Mr. Putin, playing on the others’ fears that the rebels include extremists allied with Al Qaeda, repeated his contention that the disparate opposition could not form an alternative government, according to another Western diplomat who spoke on the condition of anonymity because of the delicacy of the discussions.

Nevertheless, as those allied against Russia at the meeting noted, the summit declaration did include an implicit appeal to members of Mr. Assad’s government to abandon him, by suggesting that they could survive in a new government that excluded him. It said that public services in Syria must be preserved in a transition, and specified that “this includes the military forces and security services.”

Mr. Cameron, in a post-summit news conference, said, “For those who have been loyal to Assad but who know he has to go and who want stability in their country, they should take note of this point.”

The leaders condemned the use of chemical weapons in Syria but, again in deference to Mr. Putin, did not blame Mr. Assad for using them against the rebels as the Americans, British and French allege. It called for an “objective investigation into reports of the use of chemical weapons,” though the United States, France and Britain all claim to have hard evidence of the lethal use of such weapons to take to the United Nations.

“Both of our governments have strong evidence that in fact chemical weapons have been used in the past by the Assad regime,” Mr. Obama told reporters on Tuesday after a private meeting with President François Hollande of France. “But we are very comfortable with the approach taken by the G-8 that allows the U.N. the full powers it needs to investigate and establish these facts on the ground.”

The communiqué also evenhandedly called on both the Syrian government and opposition “to commit to destroying and expelling from Syria all organizations and individuals affiliated with Al Qaeda and any other nonstate actors linked to terrorism.”