Asked if he would tear down the prison, al-Yawir told ABC's This Week on Sunday: "No. Why? It's a prison that we spent more than $100 million building."
He acknowledged the prison was a symbol of the repressive regime of former Iraqi President Saddam Hussein, but said it would be unwise and reactionary to destroy all such symbols, given the high cost of rebuilding Iraq.
"We need every single dollar we have in order to rebuild our country instead of demolishing and rebuilding," he said.
Bush last month said the Abu Ghraib prison near Baghdad would be torn down, if the Iraqi government approved, and the US would fund the construction of a modern, maximum-security prison.
Photographs and videotapes of soldiers sexually and physically abusing and humiliating Iraqi inmates at the prison have seriously undermined US efforts in Iraq.
We have to start taking care of
all our entities, al-Yawir said
The Pentagon last week said it would widen a probe into the abuse of Iraqi prisoners to include actions of the top US commander in Iraq.
Defence Secretary Donald Rumsfeld also requested that autopsies be conducted when detainees die.
Al-Yawir said the new Iraqi government would assume control of the Abu Ghraib prison on 30 June. "We have to start taking care of all our entities," he said.
Fear of attacks
Commenting on the recent spate in assassinations and violence, al-Yawir also said there will be a "terrible" time in the country before security can be restored.
"It's going to be terrible for a while," al-Yawir said in an interview with NBC television's Meet The Press programme.
"We are committed, we are consistent and we are focused to make sure that we take necessary preparations in order to defuse the situation."
Top Foreign Ministry and Education Ministry officials were killed on Saturday and Sunday in Baghdad in what the president called "tragic" events.
"These are random killings. We hope that by re-establishing, reinstating our security forces, these things will start diminishing."