(CNN) -- A jihadist website is urging its American followers to kill comedian David Letterman, saying his tongue deserves to be cut over his remarks about a terror leader, an online intelligence group said.
The writer posted the death threat after he got upset by a Letterman joke about an al Qaeda leader killed in Pakistan, according to SITE intelligence group, which monitors and translates online terror activity.
Ilyas Kashmiri, described as al Qaeda's "military brain," died in a drone strike in June, his jihadist group said at the time.
Letterman cracked jokes about the killing, and dragged his finger across his neck to show "the way of the slaughter," the message on the jihadist site said.
He then said Kashmiri joins terror leader Osama bin Laden, who was killed in Pakistan in May, according to the message posted Wednesday.
"This despicable person mocked the leaders of the mujahideen," the post says.
The death threat urges jihadist followers to cut off Letterman's tongue and "shut it forever."
CNN could not independently confirm the message.
A spokesman for the FBI said the agency is looking into the death threats.
"In the post 9/11 world, we take all of these threats seriously," spokesman Peter Donald said.
A federal law enforcement official said such threats are common.
"We see these kinds of threats frequently against people in business and media. Usually nothing comes of them, but we check them all out," the official said.
CBS's publicity department for "Late Show With David Letterman" declined to comment Thursday on the issue.
But on the show's official Facebook page, the comedian's fans rallied to his defense.
"Keep doing what you do Dave," wrote Ronnie W., one of Letterman's supporters. "Dont let Al Quaeda influence your comedy, but Inspire it .... we got your back."
Steve Grand, director of the Brookings Institution's U.S. Relations with the Islamic World project, said that jihadists closely track U.S. culture -- as seen in seized videos showing the late Osama bin Laden watching western news programs. He said there's a sense U.S.-born cleric Anwar al-Awlaki, a prominent member in al Qaeda, may be looking to "find ways of entering the American discourse."
"There's an obsession with the United States and the West, more generally," said Grand. "And there is a desire to defend their cause through violence."
The internet serves as a motivational resource for jihadists used "to inspire offshoots and to encourage like-minded people," the Brookings' fellow added. As such, a specific threat -- like the one targeting Letterman -- could be viewed as encouraging others to act.
Yet Grand, like the federal law enforcement official, notes that dozens of such threats are made monthly. What may be more significant is how the American public reacts.
"(U.S. citizens) have gotten use to this kind of talk, and there's sort of a resilience," he said. "What is most invaluable in the United States is that the best tool against terrorism is resilience, ... to not be cowed by threats and get back to your lives."
CNN's Carol Cratty, Karen Bonsignore and Greg Botelho contributed to this report.