(CNN)Propaganda outlets linked to the Islamic State in Iraq and Syria (ISIS) have been quick to associate the group with the recent terror attacks in Orlando and Paris.
ISIS rides wave of attacks as its core territory shrinks
But the claims seem opportunistic -- and are maybe a sign of weakness rather than strength. The evidence so far suggests that in both cases the attackers had little if any connection with the group, even if they pledged allegiance to its leader, Abu Bakr al Baghdadi.
Al-Bayan, an ISIS online radio station, described Orlando gunman Omar Mateen as "one of the soldiers of the caliphate in America." A'maq, a propaganda outlet close to ISIS, said of Monday's attack by Larossi Abballa in France: "Islamic State fighter kills deputy chief of the police station in the city of Les Mureaux."
Abballa recorded a video pledging allegiance to Baghdadi at some point before or during his attack. The video was released by A'maq Tuesday, but it's unclear when it was recorded.
Neither claim indicated any prior association between ISIS and either attacker. FBI Director James Comey said Mateen had made comments supporting several Islamist movements and individuals, which "adds a little bit to the confusion about his motives."
Comey added: "So far we see no indication that this was a plot directed from outside the United States and we see no evidence he was part of any kind of network."
Regardless of the facts, ISIS is riding the wave of such terror attacks as it suffers setbacks in its core territories and a rising rate of desertions. It's been noticeably more reticent about current losses in its core territories: in Fallujah in Iraq, villages around Mosul, around Raqqa in northern Syria and Sirte in Libya.
Since its sudden surge across Iraq in 2014, ISIS has always tried to project an air of invincibility. That's perhaps why it continued the battle for the northern Syrian town of Kobane in the late summer of that year despite massive casualties. Momentum was important.
But its territorial losses have accelerated in the last six months, leading ISIS' chief spokesman and ideologue, Mohammed al Adnani, to try to reframe how ISIS defines victory. In an audio message at the end of May -- his first in seven months -- Adnani asked of the 'crusaders': "Will we be defeated and you victorious if you took Mosul or Sirte or Raqqa or all the cities -- and we returned as we were in the beginning? No, defeat is losing the will and the desire to fight."
In that same message Adnani appealed for Muslims to carry out lone-wolf attacks in the West.
"The smallest action you do in the heart of their land is dearer to us than the largest action by us," he said.
Abballa, the killer of a French police officer and his girlfriend, said he was responding to Adnani's call. Mateen said on a 911 call while inside the Pulse nightclub in Orlando, Florida, that he was pledging allegiance to ISIS. Similarly, in January 2014, Amedy Coulibaly recorded a video statement pledging allegiance to ISIS leader Baghdadi just before his gun attack on a Jewish supermarket.
Such attacks help ISIS project both influence and a sense of 'being everywhere,' boosting morale when things on the home front are not going so well. ISIS also hopes that Muslims in Europe and North America will be persecuted and distrusted, igniting a religious war.
Adnani, in an earlier message, told Europeans: "You will pay the price as you walk on your streets, turning right and left, fearing the Muslims."
What we are seeing is the evolution of a type of terrorism that has long been encouraged but not directed by both al Qaeda and ISIS: acts by individuals steeped in online self-radicalization, who adopt a cause or label based on what they've read and sometimes who they've met. Many of them don't even distinguish between ISIS and al Qaeda, even though the two groups are at war with each other.
FBI Director Comey said of Mateen: "We're highly confident this killer was radicalized at least in some part through the Internet." Found among his web browsing were the sermons of Anwar al Awlaki, the US-born al Qaeda cleric whose lectures also inspired the Tsarnaev brothers in Boston and countless other attacks.
In his ''Call to Jihad,'' recorded in 2010, Awlaki argued it was every Muslim's religious duty to kill Americans.
Mateen mentioned the Tsarnaevs during one of his 911 calls.
Last year, Muhammad Youssuf Abdulazeez, a 24-year-old from Chattanooga, Tennessee, opened fire at two military facilities, killing four Marines and a sailor. He had been watching Awlaki videos in the weeks before the shootings. And according to a federal indictment, one of the shooters in San Bernardino last year, Syed Rizwan Farook, had first been radicalized by Awlaki's sermons.
Orlando, San Bernardino, Boston: All are low-tech and random, yet devastating attacks. They are extraordinarily difficult to deter because they are unpredictable and rarely the subject of any communication. Possible suspects are "needles in a nationwide haystack," in Comey's words, motivated by a concoction of grievances, personal and political, that find meaning in the adoption of an extremist label or the sort of seductive justification for violence provided by Awlaki.
Among the thousands of open cases across the U.S. and Europe focused on would-be jihadists, discerning who might move from word to deed remains the greatest challenge. Abballa had already been convicted of helping to recruit for a jihadist network, but released after spending two years in jail.
And whatever the fate of the Islamic State's 'caliphate,' the inspiration for such attacks won't necessarily evaporate when Abu Bakr al Baghdadi is killed or Mosul captured. Anwar al Awlaki was killed in a U.S. drone strike in Yemen five years ago. But his words still drive people to kill.