As American companies prepare to bring large numbers of workers back to the office in the coming months, executives are facing one of their most delicate pandemic-related decisions: Should they require employees to be vaccinated?

Take the case of United Airlines. In January, the chief executive, Scott Kirby, indicated at a company town hall that he wanted to require all of his roughly 96,000 employees to get coronavirus vaccines once they became widely available.

“I think it’s the right thing to do,” Mr. Kirby said, before urging other corporations to follow suit.

It has been four months. No major airlines have made a similar pledge — and United Airlines is waffling.