Bush told an audience on Monday night at the Army War College in Pennsylvania that Abu Ghraib prison would be destroyed "as a fitting symbol of Iraq's new beginning".
But Ahmad Hasan al-Uqaili, deputy chief of the Human Rights Organisation in Iraq, dismissed Bush's promise as a Republican ploy "to win the [presidential] election in the United States".
Al-Uqaili said the most important thing was to end the abuses committed in the prison by both Saddam's regime and the US guards.
"The problem is not changing the location or the name of the prison," he said.
"It's about the staff of the prison. Those people are supposed to be trained in human rights. Even if a person is a prisoner, he is a human being first who must be treated with respect and dignity."
Many experts predict Bush will
lose the upcoming elections
Iraq's Deputy Foreign Minister Hamad al-Bayati said the decision to demolish Abu Ghraib "must be left to the new government" which Bush promised would be in power on 30 June.
"The recent abuses committed by US troops against Iraqi prisoners have certainly contributed to conjuring up the idea of demolishing the prison," he said.
Meanwhile, relatives of prisoners still held in Abu Ghraib prison were equally unimpressed with Bush's promise.
Speaking as she waited outside the prison complex to hear news about her husband and son, Makiya Rashid said demolishing the building did not address the issue of prisoner abuse.
"If he demolishes this prison and builds another, what's the purpose behind that? It will be the same, he will still torture our sons in it," she said.
And Amir al-Izawi - also waiting for news of an imprisoned relative - dismissed the speech by Bush as "propaganda for his election".
"If he demolishes this prison and builds another, what's the purpose behind that? It will be the same, he will still torture our sons in it"
Relative of Abu Ghraib prisoner
Bush's speech, five months before the US presidential election, was aimed at reassuring the US public as doubts rise about the war.
During his address, Bush said the US would stay in Iraq until it was free and democratic and suggested more US soldiers might have to be sent to the country.
He also briefly talked about the abuse of Iraqi prisoners at Abu Ghraib and other US-run detention facilities around the country by calling such actions the "disgraceful conduct by a few American troops who dishonoured our country".