The members of the Islamic Center of Fort Pierce had broken their fasts and left the mosque near Florida’s eastern shoreline. In the waning minutes of Sunday, less than an hour later, a surveillance camera recorded a man as he approached the mosque. Then came a flash as flames damaged the house of worship where the man who attacked an Orlando, Fla., nightclub often prayed.

The authorities, including the Federal Bureau of Investigation and the Bureau of Alcohol, Tobacco, Firearms and Explosives, were investigating the fire as a potential hate crime, even as officials cautioned that they remained uncertain about the motive.

The blaze occurred on the 15th anniversary of the Sept. 11 terrorist attacks and nearly three months after Omar Mateen opened fire at the Pulse nightclub in Orlando. It also happened around the beginning of Eid al-Adha, a Muslim holiday.

“Today was supposed to be a day of this community exchanging gifts with their kids, visiting their family members, having dinners, having lunches,” Wilfredo Ruiz, a spokesman for the mosque, said at a Monday afternoon news conference in Fort Pierce, Fla. “Instead, they needed to go to another place to worship.”