“This will be open to anyone who accepts its components,” Mr. Muñoz said. “It’s not an agreement against anyone. It’s in favor of open trade.”

On Thursday, Mr. Trump went in the opposite direction, announcing tariffs on steel and aluminum imports to the United States. He said that Canada and Mexico were being exempted for now, and that allies like Australia could later be excluded. His order could affect Brazil, China, Germany, Japan, South Korea and Turkey, though he said he would have leeway to add or take countries off the list as he sees fit.

The United States has “gone from being a leader to actually being the No. 1 antagonist and No. 1 source of fear” on trade, said Jeffrey Wilson, the head of research at Perth U.S.-Asia Center at the University of Western Australia. “If you’re a trade policy maker in Asia, your No. 1 fear is that Trump is going to take a swing at you.”

He added that such fears could prompt countries, however reluctantly, to tether themselves more closely to China. “The U.S. is really delivering the region to China at the moment,” Mr. Wilson said.

The new agreement — known as the Comprehensive and Progressive Agreement for Trans-Pacific Partnership — drops tariffs drastically and establishes sweeping new trade rules in markets that represent about a seventh of the world’s economy. It opens more markets to free trade in agricultural products and digital services around the region. While American beef faces 38.5 percent tariffs in Japan, for example, beef from Australia, New Zealand and Canada will not.

Once it goes into effect, the agreement is expected to generate an additional $147 billion in global income, according to an analysis by the Peterson Institute for International Economics. Its backers say it also bolsters protections for intellectual property and includes language that could prod members to improve labor conditions.