WASHINGTON—The White House is expected to release a plan on Sunday that would urge states to consider raising the age to buy certain firearms and would recommend that states allow school staffers to carry concealed weapons, according to White House officials who have been briefed on the proposal.

Responding to the shooting deaths of 17 people at a Florida high school last month, the plan would include President Donald Trump’s support for banning so-called bump stocks, which allow certain firearms to fire as rapidly as machine...