Seven Muslim worshipers gathered on Saturday night for an overnight spiritual retreat at the Islamic Center mosque in Escondido, Calif., about a week after dozens of Muslims were massacred thousands of miles away in New Zealand.

Shortly before dawn prayers on Sunday, someone noticed a fire outside the building, the police said. One person called 911. Someone rushed to put out the flames using a fire extinguisher. An outside wall was scorched but not badly damaged, and no one was injured. Still, harm was done: There was anti-Muslim graffiti referring to the New Zealand attack.

On Tuesday, an Escondido Police Department official, Lt. Chris Lick, said in a phone interview that the fire had been set with an accelerant. But there were no suspects, he said, and investigators were examining video surveillance “from anywhere we could get it.”

The department, which announced in a statement on Sunday that the fire was being investigated as arson and a hate crime, is working with the F.B.I., the San Diego Police Department and the Bureau of Alcohol, Tobacco, Firearms and Explosives on the case.