But terrorism researchers caution that attacks happen year-round and that there is little systematic evidence that they become more common during Ramadan. And it is almost impossible to tell what role the month plays in the thinking of individual attackers.

What is clearer is that the manipulation of the goals of Ramadan are another way in which jihadists have interpreted the religion in a way most Muslims deplore. Another example is the jihadists’ wide use of takfir, or the branding of others as infidels who deserve death. The Islamic State has used this concept to justify the killing of other Muslims, be they Shiites or fellow Sunnis whom the group deems to be insufficiently devout.

Such views course through the jihadists’ Ramadan propaganda.

In an audio message released before the month began, Abu Muhammed al-Adnani, the Islamic State spokesman, urged the group’s followers to launch attacks in the West during Ramadan in retaliation for strikes by a United States-led coalition in the group’s central territories in Syria and Iraq.

“Know that in the heart of the lands of the Crusaders there is no protection for that blood, and there is no presence of so-called civilians,” he said.

Jihadists should act, he said, “so that perhaps you will gain the great reward for martyrdom in Ramadan.”

Other propagandists reached back into Islamic history to compare the modern jihadist struggle to the Battle of Badr, a famous Ramadan victory mentioned in the Quran in which the Prophet Muhammad and his forces routed their enemies in Mecca. Some drew links between those forces and Omar Mateen, the Orlando gunman.