The meeting on Thursday assembled an A-list of Washington's brain trust - among them some of the harshest critics of the administration's Iraq policy - and included prominent Democrats as well as Republicans.
"Not everybody around this table agree with my decision to go into Iraq, I fully understand that. But these are good solid Americans who understand that we've got to succeed now that we're there," Bush said.
The president continued: "I'm most grateful for the suggestions that have been given. We take to heart the advice. We appreciate your experience and we appreciate you taking time out of your day."
Among those taking part in the meeting were Colin Powell, Bush's secretary of state during his first term, and other former secretaries of state, including Madeleine Albright, Lawrence Eagleburger and James Baker.
Spiralling violence in Iraq is a
major concern for Bush
The former defence secretaries included William Cohen, William Perry, Frank Carlucci and Harold Brown.
Bush said Condoleezza Rice, the current secretary of state and Donald Rumsfeld, the defence secretary, along with Washington's ambassador to Iraq Zalmay Khalilzad and General George Casey, the US commander in Iraq, briefed the former officials "on our strategy for victory in Iraq".
In addition to updating the former officials, "I've also had a chance to listen to their concerns, their suggestions about the way forward," Bush said.
The gathering reached back as far as the John F Kennedy administration in the 1960s, with Robert McNamara, Kennedy's defence secretary, taking part.
"It was a unique meeting," Carlucci, who served as defence secretary in the Ronald Reagan administration, told CNN television.
"I can't remember a meeting like this in recent history."
"The president participated actively in the discussion. The former secretaries expressed views, asked questions. It was a good exchange. It was all very respectful but I think people didn't hesitate to express candid views," Carlucci added.
For his part, Carlucci said: "I didn't proffer advice." But he said others at the meeting pressed the president "to continue to explain to the public what his policies are - the progress he's making, that it's a difficult task and that not everything goes perfectly.
"I think we all agreed we wanted the president to succeed. Whether we agreed he should have gone in or not. Nobody feels we need to fail at this point. We have to keep pushing ahead. There was nobody in the meeting that urged an immediate pullout."
"The president participated actively in the discussion. The former secretaries expressed views, asked questions. It was a good exchange"
Former US defence secretary
Another participant, Lawrence Eagleburger, who was secretary of state in the administration of Bush's father, George Bush Sr, told reporters outside the White House after the meeting that cementing peace in Iraq has proved to be a mammoth task.
"You've got several hundred years of antagonism between Kurds, Shias and Sunnis. Any time you think this is going to be done in a hurry, it's just not going to be the case. There will be bumps in this road," he said.
Bush said his administration was pursuing a "dual track" approach for victory over the stubborn insurgency in Iraq.
"On the one hand, we will work to have a political process that says to all Iraqis, the future belongs to you. And on the other hand, we'll continue to work on the security situation there," Bush said.
"The main thrust of our success will be when the Iraqis are able to take the fight to the enemy that wants to stop their democracy, and we're making darn good progress along those lines," Bush added.