HK GOT INT,L STRATEGIC CONSULTING LIMITED

WASHINGTON —President Obama has toured Nike’s headquarters and busy American ports in recent weeks to try to convince Democrats that rejecting the Trans-Pacific Partnership, a 12-nation trade deal that he envisions as a crucial part of a legacy of national economic revival, will undercut American power.

“If we don’t write the rules for trade around the world, guess what?” Mr. Obama warned at the headquarters of the sporting goods giant, whose wares he uses when he works out. “China will.”

Xi Jinping, the Chinese president and head of the Communist Party, is making a parallel pitch — but rooted in a very different strategy for gaining global influence. Mr. Xi has essentially shrugged off the question of whether his nation, the world’s second-largest economy, will join the pact. Instead, he has picked off American allies like Britain, Germany and South Korea to join, against the administration’s wishes, the Asian Infrastructure Investment Bank, a project started by China in part to keep its own state-owned firms busy building roads, dams and power plants around Asia.

China is at the same time setting up individual trade deals around the region so it can use its cash and enormous market leverage to strike deals more advantageous to its interests. Mr. Xi was in Kazakhstan this month plugging his “One Belt, One Road” initiative of construction from Europe to Central Asia to the seas around China.

It is a subtle form of competition, but one that many in the Obama administration see as the most important geopolitical power struggle in the world today.

“It’s not a black-and-white contest between us and China, even though the president has presented it that way to sell it to Democrats,” said Michael J. Green, a Georgetown University professor who charts the progress of the contest. “The Pacific Partnership puts pressure on the Chinese to up their game. We are somewhere between direct competition over who will make the rules and a competitive liberalization that will eventually create some common rules around the world.”

America’s strategy since the 1990s, when Bill Clinton wooed Republican votes to get China into the World Trade Organization, has been a straightforward one: Entice China into institutions that operate according to Western standards of trade rules, labor practices and the protection of intellectual property, gradually changing the way a rising power rises. Mr. Clinton made that case in visits to Beijing, arguing that if China opened its doors to trade, new ideas and the Internet would inevitably pressure its leaders toward democracy and freer expression.

It was a view that, in retrospect, overestimated American influence and underestimated the degree to which the Chinese believed they could amend the global order to suit their own economic interests. So while Mr. Obama plays the China card to sell the accord in the United States, the Chinese are pursuing their own course.

China has been excluded from the negotiations on the trade deal because it has been unwilling to sign on, so far, to the wide-ranging reforms of its economy required of all members. It could join later on — and Chinese officials have left open that possibility, as have nations like South Korea. But for now, China seems in no rush. Just as it created a new infrastructure bank to suit its own ambitions, it is assembling trade agreements whose rules it can write by virtue of the huge size of its market.

“The Chinese government’s response is to build the free-trade agreements that it can influence,” said Li Daokui, a professor at the School of Economics and Management at Tsinghua University in Beijing. “I would say it was mistake for the U.S. not to include China. If China had been allowed to join at the beginning, the landscape would be entirely different.”

Mr. Li said that if China had been part of the negotiations at the start, China might not have pushed so hard across the region for its own trade agreements, and “everything would be much simpler.”

Perhaps for Mr. Xi. For Mr. Obama, it might have been even more complex. As his failure to prevail in an important vote in the Senate on Tuesday to get the authority he needs to negotiate the trade agreement — a temporary and tactical setback, administration officials insisted — the domestic politics of this deal are difficult enough without China as a potential signatory. With China, it would be even harder.

Kevin Rudd, the former Australian prime minister, has spent the last year at Harvard and at the Asia Society studying the long-term future between China and the West. He concluded in a recently published report that in both China and the United States there was a rush “to believe that the two countries are now locked into some sort of irreversible and increasingly fractious zero-sum game.” Instead, he found the relationship was still “functioning reasonably effectively,” but noted that Mr. Xi had changed strategy.

“He has ended former paramount leader Deng Xiaoping’s foreign policy orthodoxy over the past 35 years of ‘hide your strength, bide your time, never take the lead,’ in favor of a more vigorous, activist and assertive international policy to advance Chinese interests both in the region and beyond,” he wrote in Foreign Policy.

Shi Yinhong, a professor of international relations at Renmin University, said Chinese leaders were well aware of how important approval of the trade agreement, also known as the TPP, is for Mr. Obama as he tries what he has often called a “rebalancing” toward Asia.

“The Chinese government knows the TPP is a major attempt by the U.S. to win back economic leadership in the region,” Mr. Shi said. “China also knows the Asia Pacific region is such a wide region, so you can have two stages. One is led by the U.S., which is pushing the TPP The other is dominated by China.”

Mr. Shi said China was not worried about the TPP because Asia was a vast enough region to allow for multiple trade agreements. “This is far from a zero-sum game,” he said. “In the future, both countries will find places of cooperation as well as competition.”

American officials say the Chinese view has evolved. “They have come around to seeing that they are going to have to live in a TPP world, a world with higher standards and increased competition for investment,” Michael B. Froman, the United States trade representative, who is negotiating the deal, said in an interview. “We are already seeing that investors are deciding to move to TPP countries where they will have a stable labor system,” protections for intellectual property and the freedom to move data in and out the country without government restraints, which are part of the deal being negotiated. “That’s going to force China to raise their game, too.”

Listen to the debate on Capitol Hill and it sounds a lot like the 1990s — discussion of manufacturing jobs being sent to China, fears that American sovereignty will be ignored in trade disputes, revived arguments about North American Free Trade Agreement, which was passed a quarter-century ago.

In Beijing, things sound very different. Last month, a Foreign Ministry spokesman, Hong Lei, was asked about the TPP at a regularly scheduled news conference. He responded that the TPP was one component that could help build a larger free-trade area across Asia, a plan that China laid out last year. That plan, he said, “will generate far more economic gains than all existing regional free-trade arrangements once it is completed.”