BEIJING - US Vice President Joe Biden told Chinese President Xi Jinping Wednesday that their countries' relationship will affect "the course of the 21st century" as he tried to ease tensions over an air zone declared by Beijing.

Biden's trip, which began in Japan and ends in South Korea, follows a furore over Beijing's declaration of an "air defence identification zone" (ADIZ) covering the East China Sea including islands disputed with Japan.

It demonstrates the challenges Washington - which has declared a foreign policy "pivot" towards Asia - faces in dealing with an ever more assertive China, the world's second-largest economy, while maintaining a security alliance with Beijing's great rival Japan.

"This is a hugely consequential bilateral relationship that is going to play a significant part in affecting the course of the 21st century," Biden told Xi. "This new model of major-country cooperation ultimately has to be based on trust, and a positive notion about the motive of one another."

The meeting between the two, who are said to have a good personal rapport, lasted two hours, far longer than the scheduled 45 minutes. Xi called Biden an "old friend" and told him : "You have long been committed to the growth of China-US relations and I commend you for the large amount of work you have taken."

Relations had generally maintained "positive development", he said, noting that the region and globe were undergoing "complex changes" and "regional hot spot issues keep cropping up".

It was a marked change of tone for Biden after he said at a press conference with Japanese Prime Minister Shinzo Abe Tuesday that the US was "deeply concerned by the attempt to unilaterally change the status quo in the East China Sea".

Beijing provoked widespread anger late last month by declaring an ADIZ in which all aircraft had to be subject to China's orders or face unspecified "defensive emergency measures". Washington, Tokyo and Seoul all sent military or paramilitary planes into the zone in defiance of Beijing's rules, while the US reiterated its security pact with Japan.

The decades-old argument over East China Sea outcrops which Beijing calls Diaoyu and Tokyo calls Senkaku flared after Japan bought some of the islands from their private owners in September 2012.

Meanwhile, the US vice president encouraged Chinese visa applicants to "challenge their government" during a brief meeting at the US embassy in Beijing on Wednesday.

Biden, accompanied by Ambassador Gary Locke, waved and greeted hundreds of Chinese queuing at the visa hall. "Innovation can only occur when you can breathe free, challenge the government, challenge your teachers, challenge religious leaders," Biden said.

"If you come to Washington, tell them you spoke to me here and I promise you'll be able to get to see me," Biden added, to laughter from the waiting visa applicants.