Bush said he would take the recommendations "very seriously".
The panel, co-chaired by James Baker, a former US secretary of state, said the main mission of US troops in Iraq "should evolve to one of supporting the Iraqi army, which would take over primary responsibility for combat operations".
"There is no magic formula to solve the problems of Iraq," the five Republicans and five Democrats in the group said in the report.
The study group, led by James Baker, the former US secretary of state, proposed abandoning Bush's policy of trying to isolate Syria and Iran and resuming attempts to end the Arab-Israeli conflict, which Bush has given low priority.
The White House has previously ruled out one-on-one talks with Iran about Iraq unless Tehran suspends its uranium enrichment activities.
Jalal Talabani, the Iraqi president, took issue with the report's suggestion that Iraq's problems should be tackled from a regional perspective, with neighbours Iran and Syria playing a role.
He said: "We believe that Iraq's problems can be resolved by Iraqis alone."
Talabani said Iran and Syria's co-operation should be linked to practical issues such as securing border areas rather than on political issues.
"They should not get involved in the nuts and bolts of what is happening in Iraq," he said.
Talabani's son criticised the group's view that government control in Iraq should remain centralised rather than granting more power to the regions.
Qubad Talabani, who is the Kurdistan representative in Washington, said that the recommendation alarmed many in the Kurdish north who were pushing for more autonomy.
"Many of us feel that centralised tyrannies have led us to what we have today, which is a failed state," he said, adding that he was not speaking on behalf of his father.
"They have lost all moral authority at the global level"
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The report said that oil revenues should be under central control from Baghdad: "The United States should support as much as possible central control by governmental authorities in Baghdad, particularly on the question of oil revenues." Senior Iraqi oil industry officials have pressed for Iraq's national oil company to centralise revenue distribution, but Kurdish leaders have aggressively sought independent oil asset control, the report said.
The question remains over whether the White House will take on board all 79 recommedations in the report or if they will pick and choose what they want.
Baker said that all the recommendations are equally important and that he hopes that all recommendations will be considered and implemented.
Source: Al Jazeera