"Our relationship has not been without disagreement and difficulty, but the notion that we must be adversaries is not predestined," Obama told several hundred students. He called for open dialogue but said he recognized that each nation was unique.
"I believe that each country must chart its own course," he said.
Still, Obama said, there are certain core principles that all people must share. According to the president, those principles include equal rights for everyone, a government that reflects the will of the people, open commerce and free access to information, and the rule of law.
"We do not seek to impose any system of government on any other nation, but we also don't believe that the principles that we stand for are unique to our nation," he told the gathering.
"These freedoms of expression and worship, of access to information and political participation, we believe are universal rights," Obama continued. "They should be available to all people, including ethnic or religious minorities, whether they are in the United States, China or any other nation."
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Video: Obama reaches out to Asia RELATED TOPICS Hu Jintao China Beijing World Politics Shanghai The issue of human rights has often been a sticking point between Beijing and Washington. China regularly cracks down on its religious and ethnic minorities, keeps tight reins on the media and censors the Internet.
Obama told the students that he is against censorship and is a believer in the free flow of information, calling it a "source of strength" in a democracy, despite the sting that sometimes comes with it.
"I have a lot of critics in the United States who can say all kinds of things about me," Obama acknowledged. "I actually think that that makes our democracy stronger and it makes me a better leader, because it forces me to hear opinions that I don't want to hear. It forces me to examine what I'm doing on a day-to-day basis to see if I'm doing the very best that I could be doing for the people of the United States."
The town hall meeting was shown locally on Shanghai's Phoenix TV, but it was not broadcast nationally on any of China's state-run networks. The Xinhua news agency posted a translated running transcript of the event on its Web site.
The forum also was streamed live by the United States on WhiteHouse.gov. The event was not blocked by Chinese censors to those with Internet access.
The American president told the students he welcomes a strong China, saying there are very few global challenges -- specifically referring to climate change -- that can't be solved if the United States and China work together.
Obama also fielded questions about terrorism, the war in Afghanistan and his reaction to recently being named a Nobel Peace Prize winner.
Those who took part in the forum were picked from local university students. It was not immediately clear whether the Chinese government had any role or approval in their selections.
Earlier, Obama met with Yu Zhengsheng, Shanghai's mayor and a Communist Party secretary. The president later flew to Beijing, where he will dine with Chinese President Hu Jintao ahead of formal meetings on Tuesday.
Obama's visit comes as China relishes its spot as a key global player. It is involved in major international disputes such as the showdowns with Iran and North Korea, and has used its position on the U.N. Security Council and its economic leverage to influence events around the globe.
China also is now the dominant regional player in northeast Asia, recently hosting a summit in Beijing with the Japanese and South Korean leaders.
The nation's economic expansion has led to a demand for raw materials around the world and the rapid expansion of China's presence in countries such as Guinea, Myanmar, Sudan and Venezuela. Human rights groups say China is propping up repressive regimes to secure its access to critically important raw materials.
China's rapid economic expansion outpaces growth in the United States, 8.9 percent in the past quarter versus 3.5 percent in the United States, giving Beijing huge economic leverage
Trade issues are likely to be major discussion topics during Obama's visit. The United States imports billions of dollars in Chinese products each year. He and Hu are to issue a joint statement following their talks.
Obama plans to make a side trip to the Great Wall.
The final stop of his trek is Seoul, where Obama will meet with South Korean President Lee Myung-bak, and deliver a speech to American troops at Osan Air Base.
Obama is on an eight-day journey that is taking him to Japan, Singapore, China and South Korea. He'll return to the United States on November 20.
The president left for China from Singapore, where he attended the Asia-Pacific Economic Cooperation summit and the Association of Southeast Asian Nations economic forum, and met on the sidelines with world leaders including Russian President Dmitry Medvedev.
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