Speaking on Iraq, Bush said the unpopular war there was key to promoting Middle East reforms and defeating terrorists.
"Pressure keeps the terrorists on the run, and when on the run, we're safer," he said. "We must be focused and we must not let up."
Bush, who was spoke next to John Howard, the Australian prime minister, said Australia and the US both "seek an Asia-Pacific region that is growing in freedom and prosperity and peace".
He said Asian nations should understand the importance of
fighting terrorism, since they have often been its victims.
|Bush said China should use the 2008 Olympics |
to show greater openness [GALLO/GETTY]
"Violent Islamic extremists have killed the innocent in Bali, Jakarta,
Manila, and other cities,'' he said, going on to say the fight against terrorists in Asia had been "one of the untold success stories of the war on terror".
"The rest of the world has a lot to learn from the approach to terrorism taken in this region," he said.
On the growth of democracy, Bush said Russia must "respect the checks and balances that are essential to democracy" and linked the 2008 Olympics to political reforms in China.
"Next year, China will host the Olympic Games, and it will be a moment of pride for the Chinese people. It will also be a moment when the eyes of the entire world will fall on Beijing," he said.
"We urge China's leaders to use this moment to show confidence by demonstrating a commitment to greater openness and tolerance."
On Thursday Bush held talks with Hu Jintao, the Chinese president, praising him as a leader who was "easy to talk to".
Bush, however, began his speech with a gaffe, referring to the 21-nation Apec forum as "Opec" – Organisation of the Petroleum Exporting Countries.
He quickly corrected himself, but then later in the speech went on to refer to the support given by "Austrian" troops rather than Australian troops to the war in Iraq.
In his address Bush also called on Pacific Rim nations to lead the way toward a worldwide trade agreement.
"Our challenge is to strengthen the forces of freedom and prosperity in this region," Bush said.
He said the best way to open markets was to achieve a breakthrough in global trade negotiations known as the Doha round.
"The United States is committed to seizing this opportunity - and we need partners in this region to help lead the effort," Bush said.
"No single country can make Doha a success, but it is possible for a handful of countries that are unwilling to make the necessary contributions to bring Doha to a halt."
Later on Friday, Bush is due to hold talks with Vladimir Putin, the Russian president, before attending the formal summit of Apec leaders which begins on Saturday.
The summit is expected to focus on climate change and Bush used his speech on Friday to call for greater cooperation on the issue.
Bush, however, is scheduled to leave Sydney early, before the end of the summit, in order to return to Washington to prepare for the release of a key progress report on the war in Iraq.