Biden told Xi in a 5 1/2-hour meeting and dinner with the Chinese leader Wednesday "that we don't recognize the zone, that we have deep concerns about it," a senior administration aide said in a background briefing with reporters.
"And he indicated to Xi that we are looking to China to take steps as we move forward to lower tensions, to avoid enforcement actions that could lead to crisis and to establish channels of communication with Japan, but also with their other neighbors to avoid the risk of mistake, miscalculation, accident or escalation," the aide said.
Xi was "equally clear" in explaining the Chinese view of the air identification zone over the East China Sea and an island chain, both in dispute with Japan, the aide said.
"So I think where we are on that is the Chinese have taken on board what the vice president had to lay down, and now it's a question of behavior and action as we go forward," the aide said. "And what the vice president's goal is in all of this is to ensure that we see the lowering of tensions in a way that reduces the possibility of crisis or mistake or miscalculation."
The official said Biden will "have the opportunity" to take up the issue Friday when he meets with South Korean President Park Geun-hye.
"The Koreans have -- it's not as much in the news as the Japanese concerns, but the Koreans have their own substantial concerns about this," the official said.
In a joint appearance with Biden, Xi said the China-U.S. relationship began well in 2013 and "has generally maintained a momentum of positive development."
"We're happy to see that in the recent period, our two teams have worked actively to expand coordination and collaboration on bilateral, regional and global levels," Xi said.
Landscapes within the region and internationally have undergone "profound and complex changes" recently, Xi said, citing the "in-depth readjustment" of the global economy while noting regional hot-button issues keep popping up.
He cited climate change and energy security as additional sources of concern.
"The world, as a whole, is not tranquil," Xi said. "To strengthen cooperation and dialogue is the only right choice facing both our countries."
Thanking Xi for the opportunity to meet, Biden said the new model of major-country cooperation "ultimately has to be based on trust, and a positive notion about the motive of one another."
"The relationship that you and President Obama have established thus far is full of promise and real opportunity for us," the vice president said. "If we get this relationship right with a genuine new model, the possibilities are limitless."
But as has been acknowledged in the past, Biden said the current U.S.-Chinese relationship "requires practical cooperation to deliver concrete results, and we've done much of that already."
He praised Xi for his candor because "candor generates trust," which is the basis on which constructive change is made.
Biden, on the second leg of his Asian mission, and Xi covered "every single topic in the U.S.-China relationship" during their closed-door meeting, the U.S. official said. "The conversation was very much a back-and-forth. It reflected the casual candor that the two leaders have developed."
The two also discussed North Korea and "about what the Iran example means for North Korea," the aide said, citing the combination of pressure and unity of partners that helped bring about an interim nuclear deal with the Islamic republic while negotiations about a long-term resolution concerning its nuclear program take place.
After China, Biden will visit South Korea on the final leg of his Asia visit.
Notable deaths of 2014 [PHOTOS]