TOKYO—The 11-nation free-trade group known as the Trans-Pacific Partnership said Wednesday it would open talks about admitting the U.K. as a new member, potentially adding another U.S. ally while Washington itself stays away.

The group said after an online meeting that adding the U.K.—the first potential member outside the Pacific region—would “send a strong signal to our trading partners around the world” and “help to counter protectionism and the use of unjustified trade restrictive measures.”

The TPP, which includes U.S. allies such as Japan, Canada and Australia, was originally envisioned during the Obama administration as a U.S.-led bulwark against China. One of then-President Donald Trump’s first acts in office was to withdraw from the group and its proposed free-trade deal, which Mr. Trump said would be bad for American workers.

Under Japan’s leadership, the group completed a trade deal without the U.S., which went into effect at the end of 2018. The deal eliminated most tariffs on trade between members, allowing agricultural powerhouses such as Australia to export more to Japan, while helping Japanese exports of industrial goods such as auto parts and protecting intellectual-property rights.

President Biden has shown little interest in revisiting the TPP issue, in part because free-trade deals remain unpopular among many of the swing voters whom Mr. Biden hopes to pull to his side. Secretary of State Antony Blinken said in March that people such as himself who had advocated trade deals “didn’t do enough to understand who would be negatively affected.”

Japanese officials have expressed hope that the U.S. would eventually rejoin the TPP or at least find some way to link up with the group.

The U.K. could serve as a bridge. Having left the European Union, the country is looking to do a trade deal with the U.S. in addition to pursuing TPP membership.

It applied to join the TPP on Feb. 1. The U.K.’s secretary of state for international trade, Elizabeth Truss, said membership was a “key part of our trade negotiations program as a newly independent trading nation.”

The 11 members of the TPP group, formally known as the Comprehensive and Progressive Agreement for Trans-Pacific Partnership or CPTPP, are Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore and Vietnam.

Write to Peter Landers at peter.landers@wsj.com