The Food and Drug Administration is pushing to approve Pfizer-BioNTech’s two-dose Covid-19 vaccine on Monday, further expediting an earlier timeline for licensing the shot, according to people familiar with the agency’s planning.

Regulators were working to finish the process by Friday but were still working through a substantial amount of paperwork and negotiation with the company. The people familiar with the planning, who were not authorized to speak publicly about it, cautioned that the approval might slide beyond Monday if some components of the review need more time.

An F.D.A. spokeswoman declined to comment.

The agency had recently set an unofficial deadline for approval of around Labor Day.

The approval is expected to pave the way for a series of vaccination requirements by public and private organizations who were awaiting firmer regulatory backing before implementing mandates. Federal and state health officials are also hoping that an approved vaccine will draw interest from some Americans who have been hesitant to take one that was only authorized for emergency use, a phenomenon suggested by recent polling.

Some universities and hospitals are expected to mandate inoculation once a vaccine is fully approved. The Pentagon earlier this month said it plans to make Covid vaccinations mandatory for the country’s 1.3 million active-duty troops “no later” than the middle of next month, or sooner if the F.D.A. acts earlier.

The timing of the approval could result in an uncomfortable messaging problem for the Biden administration, which on Wednesday announced that fully vaccinated people should prepare to get booster shots eight months after they received second doses. Approving the vaccine and encouraging boosters at the same time may suggest to some that the vaccine as licensed is inadequate without an extra shot.

The F.D.A. last week updated its authorizations of Pfizer-BioNTech’s and Moderna’s vaccine to allow third doses for some immunocompromised people, a decision backed by the Centers for Disease Control and Prevention.

Regulators are still reviewing Moderna’s application for full approval for its coronavirus vaccine, and a decision could come at least several weeks after the one for Pfizer-BioNTech.