Several drug makers developing Covid-19 vaccines plan to issue a public pledge not to seek government approval until the shots have proven to be safe and effective, an unusual joint move among rivals that comes as they work to address concerns over a rush to mass vaccination.

A draft of the joint statement, still being finalized by companies including Pfizer Inc., Johnson & Johnson and Moderna Inc. and reviewed by The Wall Street Journal, commits to making the safety and well-being of vaccinated people the companies’ priority….