Americans bowed their heads in silence this morning to mark the anniversary of 9/11, but the Islamist militants who follow al Qaeda's violent ideology continue to celebrate what the 2001 attacks' mastermind once declared was the "Holy Tuesday" operation.

In Pakistan, a Taliban group today heralded the devastating attacks on the U.S. 13 years ago with the twitter hashtag: #Happy9/11, which has been used by jihadist sympathizers to mock those observing the anniversary. Others are using the hashtag in apparent genuine remembrance.

British and American jihadis, who are believed to be with ISIS in Syria or Iraq or supporters with direct ties, took turns Thursday taking jabs at the painful memory of the most deadly terrorist strikes in U.S. history.

"Mujahid Miski," the suspected alias of American jihadi Mohamed Abdullahi Hassan, who is under federal indictment in Minneapolis and wanted by the FBI for joining al Qaeda affiliate al-Shabab, tweeted several taunts over 9/11 today. Miski's exact whereabouts are unknown, but he allegedly has personal ties to an American killed recently in Syria and urges fighters to wage war in Syria.

"What a beautiful sight to look at," Miski wrote regarding a photo of the twin towers exploding. "This is heart cooling for the Believers."

Over a photo of a soldier holding a folded U.S. flag, captioned, "Never Forget Sept. 11, 2001," Miski tweeted, "God willing you'll have more of them to remember soon."

Other ISIS fighters tweeted their wishes for the group to deliver an attack on America worthy of 9/11.

Every year since nearly 3,000 Americans and others perished in New York, Pennsylvania and in Virginia, al Qaeda leaders and other terrorist groups have chortled over their greatest success, and attempted to taunt Americans over what remains an open wound.

On the first anniversary in 2002, 9/11 plotter Khalid Shaikh Mohammed told Al Jazeera in an interview that he had dubbed it the "Holy Tuesday" operation because it was launched on that day of the week.

While he was held in Alexandria, Virginia's city jail for more than a year during his 2006 death penalty trial as a 9/11 conspirator, Osama bin Laden favorite Zacarias Moussaoui, would make paper airplanes and send them flying into his cinderblock cellblock walls, according to sheriff's deputies who kept watch over the al Qaeda inmate.

In court, the Frenchman would turn to the small group of relatives of those killed in the attacks who attended his trial - in which he escaped execution by one juror's vote against it - and attempted to thrust an emotional knife even deeper inside.

"I'm glad their families suffer pain," Moussaoui chortled. "I wish they'd suffer more pain."

Inside Guantanamo Bay, Cuba's controversial prison camp for alleged terrorists and Taliban, celebrations of 9/11 were typically more muted but just as taunting to their U.S. military guards.

"A couple of them would make paper airplanes and fly them around," John Bowles, who served with a naval expeditionary guard battalion at Gitmo in 2012, told ABC News. "They didn't really do much about 9/11. They'd have a little celebration by mixing up some special food. They were just more smug and happier than usual."

However, some jihadis have admitted to each other, as one put it this year, that "hope becomes buried in my heart" as the 9/11 anniversaries have passed since 2001 without a spectacular follow up - that is, until ISIS declared a caliphate this summer stretching from its strongholds in Syria and across northern Iraq.

"This year we will not be harmed if 9/11 comes and, as usual, we do not hear about an operation that shakes the earth beneath the disbelievers anywhere, because all of disbelievers [are] shaking every day due to the state of the Islamic Caliphate," a jihadi said on an ISIS-linked online forum last week.