“What can we do?” asked Fiona Hill, a Brookings Institution scholar who was the government’s top intelligence officer on Russia during the Georgia war when Mr. Putin deflected Western agitation. “We’ll talk about sanctions. We’ll talk about red lines. We’ll basically drive ourselves into a frenzy. And he’ll stand back and just watch it. He just knows that none of the rest of us want a war.”

James F. Jeffrey was Mr. Bush’s deputy national security adviser in August 2008 and the first to inform him that Russian troops were moving into Georgia in response to what the Kremlin called Georgian aggression against the pro-Moscow separatist republic of South Ossetia. As it happened, the clash also took place at Olympic time; Mr. Bush and Mr. Putin were both in Beijing for the Summer Games.

Mr. Bush confronted Mr. Putin in Beijing to no avail and then responded by ordering American ships to the region and providing a military transport to return home Georgian troops on duty in Iraq. He sent humanitarian aid on a military aircraft on the assumption that Russia would be loath to attack the capital of Tbilisi with American military personnel present. Mr. Bush also suspended a pending civilian nuclear agreement, and NATO suspended military contacts.

“We did a lot but in the end there was not that much that you could do,” Mr. Jeffrey recalled.