Historic numbers of background checks to purchase or possess a firearm were done in June, a trend in a year marked by uncertainty over the coronavirus pandemic, a subsequent economic recession, protests over racial injustice and calls to reduce police funding.

FBI numbers released Wednesday show that 3.9 million background checks were conducted last month, the most since the system was created in November 1998 to ensure felons and other prohibited people could not buy or possess a firearm. The previous monthly record came in March, when 3.7 million checks were done. Each week in June is now in...