The two-day meeting between US and Chinese officials is an expansion of discussions that the Bush administration held with Beijing on economic tensions between the two.
The dialogue now covers issues including climate change and nuclear weapons policy.
Obama urged China to work with Washington to tackle nuclear proliferation, in a pointed reference to North Korea's nuclear weapons programme.
The US and China "must continue our collaboration to achieve the denuclearisation of the Korean peninsula, and make it clear to North Korea that the path to security and respect can be travelled if they meet their obligations," he said.
The talks come as the world experiences its deepest financial crisis since the Great Depression.
"The relationship between the United States and China will shape the 21st century, which makes it as important as any bilateral relationship in the world"
Barack Obama, US president
The US is expected to have a budget deficit of about $1.84 trillion by the end of the fiscal year in September and Chinese exports have fallen.
Derek Scissors, a research fellow for Asia Economic Policy at the Heritage Foundation, said that China needs the US more than the US needs China, despite the fact that Beijing holds about $800m of US debt.
"The money to buy that debt comes from America's purchases of Chinese goods which keep Chinese employed," he said.
"So the jobs that China gets out of it are more important than the debt purchases that the US gets out of it."
Timothy Geithner, the US treasury secretary, said that the efforts of the US and China to pump billions of dollars into economic stimulus programmes signalled a turning point in relations between the countries.
China's vice prime minister said a positive relationship between Beijing and Washington would help steer the global economy towards growth.
“With the furthering of China's reform and opening up, China and the United States will have even closer economic co-operation and trade relations and [the] China-US relationship will surely keep moving forward," Wang Qishan said, adding that there are signs that the global economy was beginning to recover.
But Dai Bingguo, a Chinese state councillor, said that Beijing and Washington should not automatically rely on each other to heal the global economy.
"We are actually all in the same big boat that has been hit by fierce and huge waves," Dai said.
China and the United States must "try to cross the stormy water together as passengers" he said.
Officials from both countries have said that the dialogue is integral to building a new bilateral relationship.
Obama said he was under "no illusions that the United States and China will agree on every issue," but he said that a broadly positive relationship would be of benefit to all nations.
"The relationship between the United States and China will shape the 21st century, which makes it as important as any bilateral relationship in the world," he said.