Bush said he had shared with the Chinese president his concerns about religious freedom in China, and also the recent rash of defective Chinese-made products.
He said Hu had been "quite articulate about product safety and I appreciated his comments."
The US president added he was "anxious to accept" an invitation to attend the 2008 Olympics in China.
Both presidents are in Sydney for the weekend's annual summit of leaders from the Asia-Pacific Economic Cooperation (Apec) forum.
Hu said the two leaders had also discussed the issue of climate change, with Bush eager to see the Chinese participate in global efforts to reduce greenhouse gas emissions.
"We believe that the issue of climate change bears on the welfare of the whole humanity and sustainable development of the whole world," Hu told reporters.
He added that climate change was an issue that had to be "tackled through stronger international cooperation."
The meeting between Bush and Hu came as news emerged of an embarrassing breach of the massive security operation put in place for the Apec meeting.
|Authorities have spent millions of dollars |
on security for the summit [Reuters]
The breach was carried out by members of an Australian TV comedy show - one of them dressed as Osama bin Laden - who drove through two security checkpoints in a fake motorcade carrying Canadian flags.
The group came within meters of the hotel where the US president is staying before they were arrested by police.
Australian authorities have spent an estimated $150m on security for the Apec meeting, in what they say is the biggest such operation ever mounted in the country.
There are about 5,000 police as well as members of the special forces deployed in and around the city.