"That (a timetable) would embolden the terrorists and make them believe they can wait us out," Bush said in his State of the Union address late on Wednesday.
"In the end, Iraqis must be able to defend their own country - and we will help that proud, new nation secure its liberty," the president said 22 months after he ordered the invasion of Iraq.
Speaking to a joint session of the US Congress and a television audience of millions, Bush laid out plans to spread "democracy in the Middle East".
But his refusal to set a timetable for US troops withdrawal from the war-torn country drew a wave of criticism.
The New York Times said hinging US withdrawal from Iraq on training better Iraqi security forces "is absolutely not enough" without demanding maximum effort from the new government in creating a state "that recognises the rights and needs of all its citizens".
There are around 150,000 US
troops currently stationed in Iraq
In his speech, the US president said: "We will increasingly focus our efforts on helping prepare more capable Iraqi security forces, forces with skilled officers, and an effective command structure.
"As those forces become more self-reliant and take on greater security responsibilities, America and its coalition partners will increasingly be in a supporting role."
The daily said Bush's insistence that it was inappropriate to set a timetable for withdrawal "obscures the very immediate need to set goals, and to make it clear to the Iraqis that the continued presence of American forces depends on their meeting those goals".
The Times branded Bush's speech as "yet another feel-good paean to freedom and democracy that did little to show the American people an exit strategy for United States troops, or to show the Iraqis what we expect from them next".
Speaking to Aljazeera from Washington, Dr Munzir Sulayman, an expert in political affairs, said there had been a desire to set up a strategy for the withdrawal of US forces from Iraq two months after the elections but Bush did not say that publicly as it would be a made-up timetable.
"It is absolutely clear that Bush is afraid of what is coming next but he did not frankly say that," said Sulayman.
"There are not enough assurances to carry out [withdrawal] arrangements after the elections," he told Aljazeera.