"The major challenges of the 21st Century from climate change to nuclear proliferation to economic recovery are challenges that touch both our nations, and challenges that neither of our nations can solve by acting alone," he said.
With world leaders meeting in Copenhagen next month to discuss how to tackle global warming, climate change is perhaps the most pressing issue to resolve.
Mr Obama appeared to raise hopes that a deal could be struck in Copenhagen.
"Our aim there is not a partial accord or a political declaration, but rather an accord that covers all of the issues in the negotiations and one that has immediate operational effect," said Mr Obama.
The comment seemed to be at odds with a much less ambitious statement from world leaders, including Mr Obama and Mr Hu, on Saturday at the Asia-Pacific Economic Co-operation (Apec) forum.
Standing next to President Hu, Mr Obama also took up a theme that has previously proved contentious between the two countries.
He said China should resume talks with representatives of Tibet's exiled leader the Dalai Lama to resolve differences over the Himalayan region.
China says the Dalai Lama is trying to split Tibet from the rest of the country and last year said previous talks had achieved nothing.
President Hu said China and the US would hold talks about human rights and religious freedom.
But, in an indication of China's rising power and influence, he said the two counties should now treat each other as equals.
"We will continue to act in a spirit of equality, mutual respect and non-interference in each other's internal affairs," said Mr Hu, who spoke first at the media event.
He added that "trade friction", which has recently increased between China and the United States, should be resolved on an "equal footing".
"I stressed to President Obama that under the current circumstances our two countries need to oppose all kinds of trade protectionism even more strongly," he said.
Later in the day, Mr Obama met the chairman of China's parliament, Wu Bangguo, and attended a state banquet.
The US leader, who is not being accompanied by his family on the tour of China, is also fitting in visits to the Forbidden City and the Great Wall of China.
Mr Obama earlier visited Japan and Singapore on what is his first visit to Asia as US president. He is scheduled to fly to South Korea after leaving China on Wednesday.
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