WASHINGTON—The emerging fault lines in the global trading system were laid bare Tuesday, as 11 Pacific Rim nations agreed to forge a new commercial bloc that excludes the U.S., while President Donald Trump signed orders to curb cheap Asian imports he said had unfairly harmed American manufacturers.

As Mr. Trump touted from the Oval Office his commitment “to defending American companies…very badly hurt from harmful import surges,” U.S. allies grew more vocal in their concerns about what they view as the longtime leader of the world trading system turning inward.

“Now in some parts of the world, there is a move toward protectionism,” Toshimitsu Motegi, the Japanese economy minister, said in Tokyo, announcing the agreement of the Trans-Pacific Partnership, redrafted after Mr. Trump pulled the U.S. out a year ago. “TPP-11 is a major engine to overcome such a phenomenon.”

The debate is expected to intensify this week as it shifts to Davos, Switzerland, where Mr. Trump is scheduled Friday to explain and defend his emerging “America First” policies to the World Economic Forum, a group that has staunchly defended and fostered globalism over the past four decades.

As a sign of the arguments to come, Prime Minister Narendra Modi of India addressed the forum Tuesday with a speech that didn’t mention Mr. Trump by name, but appeared aimed at him.