Delivering his annual State of the Union address, Bush also said the elections in Iraq marked a "new phase" in US efforts to train Iraqi security forces and that both liberty and democracy were on the march in the region.
"The goal of two democratic states, Israel and Palestine, living side by side in peace is within reach - and America will help them achieve that goal," Bush told the joint session of the US Congress and a televised audience of millions.
With an eye on his place in history, Bush said spreading democratic reforms in the Middle East would help defeat "terrorists like those behind the September 11, 2001 attacks".
Exulting over elections in Iraq, the president said that Washington's campaign to build democracy there "will succeed because the Iraqi people value their own liberty - as they showed the world last Sunday".
"Our generational commitment to the advance of freedom, especially in the Middle East, is now being tested and honoured in Iraq," he said.
Buoyed by the poll, Bush pledged
to train more Iraqi troops
"The new political situation in Iraq opens a new phase of our work in that country ... we will increasingly focus our efforts on helping prepare more capable Iraqi security forces - forces with skilled officers, and an effective command structure," he said.
"In the end, Iraqis must be able to defend their own country - and we will help that proud, new nation secure its liberty," he promised.
However, he refused to set a specific timetable for American withdrawal from Iraq.
"We will not set an artificial timetable for leaving Iraq because that would embolden the terrorists and make them believe they can wait us out," he said.
Appeal to allies
Bush also made an unusual appeal to allies such as Egypt and Saudi Arabia to pursue political reforms while warning Syria and Iran to stop backing terrorism.
"The goal of two democratic states, Israel and Palestine, living side by side in peace is within reach - and America will help them achieve that goal"
US President George Bush
"To the Iranian people, I say tonight: 'As you stand for your own liberty, America stands with you.'
"The government of Saudi Arabia can demonstrate its leadership in the region by expanding the role of its people in determining their future. And the great and proud nation of Egypt, which showed the way toward peace in the Middle East, can now show the way toward democracy in the Middle East," he said.
The annual address came two weeks after Bush vowed at his inauguration to spread democracy across the world.
The US president also said he was working with Asian partners to convince North Korea to end its nuclear weapons programme.
"We are working closely with governments in Asia to convince North Korea to abandon its nuclear ambitions," he said.