"I believe that we are poised to make steady progress on some of the most important issues of our times," the president told diplomats from both countries assembled in the vast hall of the Ronald Reagan Building.
Obama said he was under "no illusions that the United States and China will agree on every issue" but he said closer cooperation in important areas was critical for the world.
"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," Obama said.
The discussions in Washington represent the continuation of a dialogue begun by the Bush administration, which focused on economic tensions between the two nations. Obama chose to expand the talks to include foreign policy issues as well as economic disputes over trade and currency values.
Secretary of State Hillary Rodham Clinton, welcoming the Chinese, said the two nations were "laying brick by brick the foundation for a stronger relationship."
Treasury Secretary Timothy Geithner and Vice Premier Wang Qishan, China's top economic policymaker, both spoke of hopeful signs that the global economy was beginning to emerge from its worst financial crisis since the Great Depression.
Geithner said that the so far successful efforts of the two economic superpowers to move quickly to deal with the downturns with massive stimulus programs marked a historic turning point in the relationship of the two nations.
Speaking through a translator, Wang said that "at present the world economy is at a critical moment of moving out of crisis and toward recovery."
State Councilor Dai Bingguo said that the two countries were trying to build better relations despite their very different social systems, cultures, ideologies and histories.
"We are actually all in the same big boat that has been hit by fierce wind and huge waves," Dai said of the global economic and other crises.
Obama said that the United States and China have a shared interest in clean and secure energy sources.
As the world's largest energy consumers, Obama said that neither country profits from a dependence on foreign oil. He also said neither country will be able to combat climate change unless they work together.
However, the discussions this week were not expected to bridge wide differences between the two nations on climate change and officials cautioned against expecting any major breakthroughs in other areas either. U.S. officials said they hoped the talks would set a positive framework for future talks.
The administration did praise China for the help it has provided in the nuclear standoff with North Korea.
With the global economy trying to emerge from a deep recession, the United States and China have enormous stakes in resolving tensions in such areas as America's huge trade deficit with China and the Chinese government's unease over America's soaring budget deficits.
Three years ago, then-Treasury Secretary Henry Paulson used the initial U.S.-China talks to press Beijing to let its currency, the yuan, rise in value against the dollar to make it cheaper for Chinese to buy U.S. goods. U.S. manufacturers blame an undervalued yuan for record U.S. trade deficits with China - and, in part, for a decline in U.S. jobs.
The U.S. efforts have yielded mixed results. The yuan, after rising in value about 22 percent since 2005, has scarcely budged in the past year. Beijing had begun to fear that a stronger yuan could threaten its exports. Chinese exports already were under pressure from the global recession.
But the Obama administration intends to remain focused on the trade gap, telling Beijing that it can't rely on U.S. consumers to pull the global economy out of recession this time. In part, that's because U.S. household savings rates are rising, shrinking consumer spending in this country.
For the United States, suffering from a 9.5 percent unemployment rate, the ultimate goal is to help put more Americans to work.
While the U.S. trade deficit with China has narrowed slightly this year, it is still the largest imbalance with any country. Critics in Congress say that unless China does much more in the currency area, they will seek to pass legislation to impose economic sanctions on Beijing, a move that could spark a trade war between the two nations.
For their part, Chinese officials are making clear they want further explanations of what the administration plans to do about the soaring U.S. budget deficits. China, the largest foreign holder of U.S. Treasury debt - $801.5 billion - wants to know that those holdings are safe and won't be jeopardized in case of future inflation.
Geithner said in his opening remarks that the United States was moving to repair its financial system and overhaul how financial companies are regulated. He said the administration was also determined to deal with a budget deficit projected to hit $1.84 trillion this year, more than four times the previous high.
"We are committed to taking the necessary steps to bringing our fiscal deficits down to a more sustainable level," he said.
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Associated Press writers Foster Klug and Steven Hurst in Washington and Joe McDonald in Beijing contributed to this report.
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