TOKYO — President Biden has enlisted a dozen Asia-Pacific nations to join a new loosely defined economic bloc meant to counter China’s dominance and reassert American influence in the region five years after his predecessor withdrew the United States from a sweeping trade accord that it had negotiated itself.

The alliance will bring the United States together with such regional powerhouses as Japan, South Korea and India to establish new rules of commerce in the fastest-growing part of the world and offer an alternative to Beijing’s leadership. But wary of liberal opposition at home, Mr. Biden’s new partnership will avoid the market access provisions of traditional trade deals, raising questions about how meaningful it will be.

“We’re writing the new rules for the 21st-century economy,” Mr. Biden said on Monday in Tokyo during the launch for what he has termed the Indo-Pacific Economic Framework. “We’re going to help all of our country’s economies grow faster and fairer.”

The president sat alongside Prime Minister Narendra Modi of India and Prime Fumio Kishida of Japan for the rollout of the initiative, while other leaders joined the event by videoconference. The new alliance represents the centerpiece not only of Mr. Biden’s first trip as president to Asia but also of his broader strategy in the region at a time when China has increasingly filled the void left when President Donald J. Trump pulled the United States out of the Trans-Pacific Partnership in 2017.

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