Giving no ground, Chinese President Xi Jinping and U.S. Vice President Joe Biden traded strong arguments Wednesday about China’s contentious new air defense zone, with no indication of progress toward defusing a situation that is raising anxieties across Asia and beyond.

Though Biden made clear the deep concern of the U.S. and other countries during the 5 ½ hours of talks — themselves highly unusual for an American vice president and Chinese president — Xi vigorously made his case, too, for China’s declaration of new rules concerning a strip of airspace more than 600 miles long above disputed islands in the East China Sea.

The U.S. worries that China’s demand that pilots entering the airspace file flight plans with Beijing could lead to an accident or a confrontation spiraling dangerously out of control. Now it is up to the Chinese to take steps to lower tensions, and “it’s a question of behavior and action,” said a U.S. official, who briefed reporters on the private talks.

The official was not authorized to be quoted by name and spoke only on condition of anonymity.

Though Biden expressed no disappointment in public remarks, the outcome of his visit was not what the U.S. might have hoped for.

A day earlier, the vice president had stood shoulder to shoulder in Tokyo with the leader of Japan, China’s regional rival, pledging to raise Washington’s concerns with Xi directly. But as he arrived in Beijing, an editorial in the state-run China Daily charged Washington with “turning a blind eye to Tokyo’s provocations,” warning that Biden would hit a dead end should he come “simply to repeat his government’s previous erroneous and one-sided remarks.”

Late Wednesday in Washington, Defense Secretary Chuck Hagel called China’s announcement of the zone “destabilizing” and complained that it had come “so unilaterally and so immediately without any consultation.”

“That’s not a wise course of action to take for any country,” Hagel said at a Pentagon news conference.

Neither Biden nor Xi mentioned the dispute as they appeared briefly before reporters at the end of their first round of talks. But in private, the issue came up at length at the beginning and again near the end of the long-planned meeting, senior Obama administration officials said.

The typically upbeat Biden appeared subdued as he reflected on the complexity of the relationship between China and the U.S., two world powers seeking closer ties despite wide ideological gulfs they have as of yet been unable to bridge.

“This new model of major-country cooperation ultimately has to be based on trust, and a positive notion about the motive of one another,” Biden said, flanked by top advisers in a resplendent meeting room steps away from Tiananmen Square.

The calibrated public comments played down the deep strains permeating the relationship between the world’s two largest economies.

Earlier, however, Biden told Chinese youngsters waiting to get visitor visas processed at the U.S. Embassy that American children are rewarded rather than punished for challenging the status quo, an implicit criticism of the Chinese government’s authoritarian rule.

“I hope you learn that innovation can only occur where you can breathe free, challenge the government, challenge religious leaders.” Biden said.

Xi, for his part, stuck to the script — at least in public. The Chinese leader touted the benefits of closer U.S.-China ties as he laid out “profound and complex changes” underway in Asia and across the globe.

“The world, as a whole, is not tranquil,” Xi said.