Kicking off a new dialogue with Beijing, Clinton said that the two "are laying brick by brick the foundation of a stronger relationship."
She said it was time to move from "a multipolar world to a multipartner world."
The talks will include discussions of the global economic slide, climate change and commercial relationships. Clinton said the two "will not always see eye to eye." Both sides are emphasizing the importance of the meetings.
President Obama meanwhilewill shape the history of the 21st century.
"I believe that we are poised to make steady progress on some of the most important issues of our times," Mr. Obama said.
Top officials said they saw hopeful signs that the global economy was beginning to move into a period of recovery.
Treasury Secretary Timothy Geithner said that the joint efforts of the nations to deal with the financial crisis with large stimulus programs marked a turning point in the relationship of the two economic superpowers.
Chinese Vice Premier Wang Qishan said that "at present the world economy is at a critical moment of moving out of crisis and toward recovery."