In an interview with NPR radio that is due to be broadcast on Wednesday, Lugar urged Bush to co-operate with US parliamentarians on the future of US involvement in Iraq.
That would be a tragedy for the troops, a tragedy for Iraq, a tragedy for us.
Richard Lugar, senior Republican senator
"The president may believe that he can simply continue on with or without the congress, but I think he is wrong in that assumption.
"My fear is that at some point we will have a withdrawal from Iraq that is very disorderly and not very well planned," he said in excerpts released by the station.
"That would be a tragedy for the troops, a tragedy for Iraq, a tragedy for us."
In a US senate speech on Monday, Lugar said US policy was limiting America's diplomatic effectiveness around the world and straining the US military.
"The costs and risks of continuing down the current path outweigh the potential benefits that might be achieved," he said.
Voinovich, whose Ohio state which has borne a heavy price in US combat deaths in Iraq, said:
"We must not abandon our mission, but we must begin a transition where the Iraqi government and its neighbours play a larger role in stabilising Iraq."
Tony Snow, a White House spokesman, played down Lugar's intervention, saying it was important to give the surge strategy time to succeed.
|Richard Lugar is a respected figure in|
US foreign relations [EPA]
"Dick Lugar is a serious guy, so obviously you take it seriously. But on the other hand, again, he voted against the surge," Snow said.
Seventy-five US soldiers have died in Iraq this month alone, and the total toll since the 2003 invasion has hit 3,552, according to the Pentagon.
Lugar's and Voinovich's comments hinted at a softening of Republican backing used by Bush as a bulwark against attempts by the Democratic-led congress to end the war.
Democratic senate leaders, lacking the 60 votes needed to force Bush's hand, argue that congress will only have a decisive impact when Republicans desert the president on the war.
Harry Reid, the senate Democratic leader, seized on Lugar's remarks.
"When we finally end this war, and the history books are written, I believe that senator Lugar's words yesterday could be remembered as a turning point." he said.