Bush made the statement in a speech and question-and-answer session at a World Affairs Council event on Monday.
He predicted that fighting would not end with Thursday's parliamentary elections and said much work remains to make Iraq's democracy inclusive to all.
Bush said elections on 15 December would help the country mark a turning point in the Middle East.
He denounced the presence of prisons in Iraq where men, mostly Sunni, were being held and apparently beaten and tortured.
Bush said: "This conduct is unacceptable, and the prime minister and other Iraqi officials have condemned these abuses, and an investigation has been launched and we support these efforts."
"Those who committed these crimes must be held to account."
Earlier on Monday, the Iraqi government said 13 prisoners found in a prison in Baghdad, in addition to a secret bunker found last month and operated by the Interior Ministry, showed signs of abuse.
Bush needs a relatively smooth showing during Thursday's elections in Iraq to hold up as a sign of progress so he can counter the daily news of bombings and US troop deaths that have soured the American public's view of the war.
Bush is fighting to get his second term back on track after a year in which Americans lost faith in his ability to manage the war and a growing number came to believe his administration misled them in making the case for the US-led invasion.
"No nation in history has made the transition to a free society without facing challenges, setbacks and false starts"
"No nation in history has made the transition to a free society without facing challenges, setbacks and false starts," Bush said.
"It's a remarkable transformation for a country that has virtually no experience with democracy and which is struggling to overcome the legacy of one of the worst tyrannies the world has known," he said.
The speech was Bush's latest attempt to try to bolster support for his Iraq strategy among Americans sceptical of his leadership.
Speaking at an event hosted by the World Affairs Council, a private, non-profit, non-partisan educational organisation, Bush repeated: "We will accept nothing less than complete victory."
According to the Pentagon, 2138
US personnel have died in Iraq
His figure for the death toll among Iraqis was in the range given by Iraq Body Count, a US-British non-government group, which currently says between 27,383 and 30,892 civilians, rather than all Iraqi citizens, have been killed in Iraq since the invasion.
Its figures are based on media reports, which often fail to capture all the deaths in the country.
Other estimates, including one done by scientists and published in the medical journal Lancet, put the civilian death toll at as high as 100,000.