Barack Obama has held a summit in Beijing with Chinese leader Hu Jintao, as he continues his first tour of Asia as US president.
Mr Obama was given an official welcome in the Great Hall of the People, or parliament, before going for talks with the Chinese president.
Trade, climate change and economic issues are expected to dominate.
The two men have already met during the visit, having dinner together on Monday in the Chinese capital.
Before Tuesday's closed-door meeting began, Mr Obama said: "We believe strong dialogue is important not only for the US and China, but for the rest of the world."
Mr Hu said: "I look forward to having an in-depth relationship."
Later in the day, Mr Obama is due to meet the chairman of the parliament, Wu Banguo, and there will be a state banquet at the Great Hall.
The US leader, who is not being accompanied by his family on the tour, is also fitting in visits to the Forbidden City and the American embassy.
He arrived by plane in the capital from Shanghai where he had addressed Chinese students, telling them that individual rights and freedoms should be available to all.
Mr Obama had told his audience that he was a "big supporter of non-censorship", and that unrestricted internet access was a "source of strength" that should be encouraged.
Communist China employs some of the tightest controls over internet content in the world.
Greeting his American guest in Beijing on Monday, President Hu noted Mr Obama's meeting with the students, calling it "quite lively".
Mr Obama smiled broadly as his host spoke, then told Mr Hu that the world recognised "the importance of the US-Chinese relationship" in tackling global problems.
During the two leaders' dinner, conversation centred upon the respective histories of the two countries, and both men outlined the economic challenges their states face.
They swapped ideas about the significance education plays in the advancement of their people, the Associated Press news agency reports.
Mr Obama visited Japan and Singapore earlier and is scheduled to fly to South Korea after leaving China on Wednesday.