U.S. Steel is an iconic example of the lost manufacturing muscle that President Biden says his economic policies will bring back to the United States.

But last month, the storied-but-diminished company announced plans to be acquired by a Japanese competitor. That development has put Mr. Biden in an awkward bind as he tries to balance attempts to revitalize the nation’s industrial sector with his efforts to rebuild international alliances.

Mr. Biden’s administration has expressed some discomfort with the deal and is reviewing the proposed $14.1 billion takeover bid by Japan’s Nippon Steel. The company is offering a hefty premium for U.S. Steel, which has struggled to compete against a flood of cheap foreign metal and has been weighing takeover offers for several months.

The proposal has quickly become a high-profile example of the difficult political choices Mr. Biden faces in his zeal to revive American industry, one that could test the degree to which he is willing to flex presidential power in pursuit of what is arguably his primary economic goal: the creation and retention of high-paying union manufacturing jobs in the United States.

Mr. Biden is under pressure from the United Steelworkers union and populist senators from both parties, including Democrats defending crucial swing seats in Ohio and Pennsylvania this fall, to nix the sale on national security grounds. The senators contend that domestically owned steel production is critical to U.S. manufacturing and supply chains. They have warned that a foreign owner could be more likely to move U.S. Steel jobs and production overseas.

“This really should be a no-brainer,” Senator Josh Hawley, Republican of Missouri, said in an interview last week. “I don’t know why it would be difficult to say, my gosh, we’ve got to maintain steel production in this country, and particularly a company like this one, where you have thousands of workers in good union jobs.”