U.S. President Barack Obama and Chinese President Hu Jintao, seeking a steadier footing for the often-troubled U.S.-China relationship, played up the two nations' common interests—and soft-pedaled or ignored longstanding issues that divide them.

Their uneasy balance—neither friend nor foe—is emerging as the operating principle behind the globe's most critical bilateral relationship. In a one-hour press conference in the White House's East Room, the two leaders sought to demonstrate they can live with areas of tension, even if they can't cure them, including China's currency policy, its human-rights record and the nuclear ambitions of North Korea.

In private sessions, senior administration officials said, the two leaders addressed some of the countries' friction points: They spent about half their time discussing economic issues, and the rest on Iran, North Korea, human rights and other areas, aides said. President Obama's aides said that he pressed Mr. Hu more gently than Congressional critics did on letting China's currency rise, noting it has gradually risen 3.5%, and more if inflation is accounted for. "But he said that China needs to do more, needs to move faster," said a senior aide.

On North Korea, Obama aides also noted that China agreed on the need to press that nation to curtail uranium enrichment that could enhance its nuclear weapons capability, a point made in a U.S.-China communiqué.

An expansive reception of Mr. Hu at the White House, which included a private dinner with Mr. Obama on Tuesday night and formal state dinner on Wednesday, reflected the changing nature of U.S.-China relations. During the previous two visits of Chinese leaders to White House, China was clearly the junior partner and treated as such. That's no longer the case, as China has grown to the top echelon of economies and become the U.S.'s largest banker, as well as competing for political and commercial influence in Asia, Latin America and Africa.

Underscoring its rapid economic advance, China reported early Thursday in Beijing that its gross domestic product grew 10.3% in 2010, faster than many economists expected and well over twice the likely pace of the U.S. The latest data make it highly likely that China surpassed Japan as the world's No. 2 economy in 2010—although Japan's full year data hasn't been issued yet. When Mr. Hu last visited the White House five years ago, China was the world's fifth-biggest economy, less than half its current size.

The visit comes at a time when Americans are worried they may be slipping behind in global competition with China. In a new Wall Street Journal/NBC News poll, Americans were asked which country they thought would be the world's leading nation in 20 years—and 38% named China, while 35% named the U.S.

Both leaders found themselves trying to look strong domestically while assuaging audiences overseas. Mr. Obama tried to calm Chinese fears that the U.S. is trying to block that nation's ascent while he pitched Americans on the economic value of the Chinese relationship. To make the latter point, the administration announced Chinese approval of export purchases valued at $45 billion—though some of those had been announced before.

"I absolutely believe that China's peaceful rise is good for the world and it's good for America," President Obama said in a statement aimed at Beijing. Then he followed with a made-in-America message: "We want to sell you all kinds of stuff," he said to Mr. Hu.

The U.S. president, a Nobel Peace prize winner, pointedly didn't make reference to China's jailing of the award's most recent recipient, Liu Xiaobo. His aides said Mr. Obama pressed the Chinese dissident's case in the day's private meetings. In public, however, he sought to play up areas of agreement.

For the Chinese public and factions in the Chinese government wary of the U.S., Mr. Hu repeatedly stressed that Beijing is being treated as an equal and with "mutual respect and mutual benefit." For the U.S. audience, he avoided mentioning a slew of outstanding issues that rankle Beijing, including worries over the safety of China's nearly $900 billion horde of Treasurys and the Federal Reserve's ultra-low interest-rate policy, which can feed real-estate bubbles and inflation in China.

In one surprising nod to U.S. public opinion, Mr. Hu said "a lot still needs to be done in China in terms of human rights," a comment Obama advisers called a significant admission.

In 1997, President Jiang Zemin used his formal state visit— China's most recent until this one—to lobby the U.S. to support China's admission into the World Trade Organization. In 2006, Mr. Hu used his stop in the Bush White House to try to shore up his position back home among Beijing's many factions, but was weakened by a series of perceived slights. Those included President Bush's decision to host a working lunch rather than a state dinner.

This time, in the press conference, Mr. Hu brushed off the decisions by Senate Majority Leader Harry Reid (D., Nev.) and Speaker of the House John Boehner (R., Ohio) not to attend the dinner, an unusual although not unprecedented move. "As to who will attend, who will not attend and for what reasons, I think President Obama is certainly in a better position to answer that question," he said in a rare moment of levity.

Still, anti-China rumblings from Capitol Hill, where Mr. Hu was to meet lawmakers Thursday, underscored deeper tensions. Lawmakers at a House foreign affairs panel hearing Wednesday, called to coincide with Mr. Hu's visit, castigated the Chinese leader for being a "dictator" of a "gulag state." Critics from both parties aimed at Beijing trade practices they said were purposefully damaging the U.S.

In the meeting of the two presidents and their aides, it was the U.S. largely doing the asking for favors—pressing China to sign deals and ease restrictions on U.S. companies doing business in China. With just a year left in his presidency, Mr. Hu seemed satisfied to be treated as an equal partner, though he reiterated the need for cooperation on a slew of issues.

U.S. negotiators spent weeks trying to line up Chinese purchases and investments that the White House could announce. In some instances, the announcements clearly reflected old news. China gave final approval to the sale of 200 aircraft, which had been booked as early as 2007.

U.S. corporate chiefs meeting at the White House with Mr. Hu barely mentioned the yuan-dollar exchange rate, which the U.S. believes is kept artificially low to aid Chinese exporters. Instead, they voiced frustration over other Chinese policies preventing their ability to win access to the market, from government procurement restrictions to caps on exports of rare-earth materials.

John Frisbie, president of the U.S.-China Business Council, a trade organization, said the most significant trade policy announcement was one known as a "delinking": China will issue rules assuring foreign firms that they can bid for Chinese government procurements even if the technology involved isn't developed in China. Foreign firms have complained that Beijing had essentially used "Buy China" regulations to bar foreign firms from high-technology projects.

In Mr. Obama's public statements and private meetings with Mr. Hu, the U.S. president placed the currency issue in the context of the broader U.S.-China economic relationship. Treasury Secretary Timothy Geithner estimates with the effects of different levels of inflation in the U.S. and China, the yuan is now advancing at a roughly 10% clip.

On human rights, Mr. Obama said the U.S. stood for fundamental freedoms and would press China on these issues. But along with not mentioning jailed dissident Mr. Liu publicly, he defined human rights broadly to include those lifted out of poverty by China's rapid growth—a point Chinese officials regularly make.

"We believe part of justice and part of human rights is people being able to make a living and having enough to eat and having shelter and having electricity," Mr. Obama said. In what appeared to be a technical glitch, one of many during the press conference, Mr. Hu at first didn't answer a reporter's question on China's human-rights record.

But then he said China would "continue efforts "to improve the lives of the Chinese people, and we will continue our efforts to promote democracy and the rule of law in our country," and continue to discuss human rights.