LONDON--The Islamic State extremist group has sought to link itself to Sunday’s attack in Garland, Tex., during which two assailants shot a security guard before being killed by police officers outside an event devoted to cartoons depicting the Prophet Muhammad, a group that monitors extremist activity online reported on Tuesday.

The Islamic State, which is waging an insurgency in Syria and Iraq, said on its official radio station Al Bayan that “two soldiers from the soldiers of the caliphate” had carried out the attack, according to the SITE Intelligence Group, which quoted the Islamic State as saying that the two soldiers attacked an exhibit “holding a contest for drawings offensive to the Prophet Muhammad.”

The news item from the Islamic State warned that the United States would see “from the soldiers of the Islamic State what will hurt you, Allah permitting,” SITE said.

The statement provided few details, however, and it remained unclear whether the extremist group was in fact involved even indirectly in the attack or whether it was making the claim purely for propaganda value, following a pattern of trying to attract recruits by praising terrorist attacks against Western targets for which it may have provided ideological inspiration rather than weapons or training.

Although the Islamic State, also known as ISIS or ISIL, is seen as well organized in the territory in Iraq and Syria where it has declared a caliphate, or Islamic state, there is little evidence that it has actively planned and directed attacks abroad.

“Normally, it is sufficient for a person to say they are affiliated with ISIS even if they haven’t been trained by ISIS, as it is in keeping with ISIS’ call for people to carry out attacks on the west,” said Aymenn Jawad al-Tamimi, a researcher at the Interdisciplinary Center in Herzliya, Israel, who studies the Islamic State. “It is not as if ISIS has a cell in the United States or trains people. This is not ISIS coming to America.”

In voice recordings released online, Islamic State leaders have called on their followers to launch attacks on “infidels” wherever they may be, by running them over with cars, stabbing them or throwing them off cliffs. Most attacks associated with the group outside Islamic State territory appear to have been planned and executed at the local level with little more than inspiration provided by the organization.

The little information publicly available about the attackers in Texas suggests that they had been influenced by different currents of jihadist thought. A Twitter account believed to be associated with the gunmen used a profile picture of Anwar al-Awlaki, a Yemeni-American cleric who had been with Al Qaeda before he was killed in an American drone strike in Yemen in 2011.

But a post from the same account pledged fealty to Abu Bakr al-Baghdadi, the head of the Islamic State, which has broken with Al Qaeda and competes with it for prestige and recruits.

In its statement on Tuesday, the Islamic State was quoted by SITE as saying that future attacks on Americans would be “worse and more bitter.”

American law enforcement officials are still trying to piece together whether others were behind the attack that was carried out by two men, Elton Simpson, 30, and Nadir Hamid Soofi, 34, in Garland, a suburb of Dallas. The authorities have started to examine the backgrounds of the two men, who lived in the same apartment complex in Phoenix.

One has been identified by the F.B.I. as a jihadist terrorism suspect who regularly attended a mosque in Phoenix. The other ran a carpet cleaning business and also attended a mosque.

The event at which the attack took place included a contest for the best caricature of Muhammad, with a top prize of $10,000.

The Texas attack bore some resemblance to January’s attack by Islamic extremists on the offices in Paris of the satirical newspaper Charlie Hebdo, during which 12 people, including several cartoonists, were killed after the newspaper published cartoons lampooning Muhammad. However, in the Texas shooting, only the gunmen were killed.

After January’s terrorist attacks in and around Paris, during which Amedy Coulibaly, a French citizen of African descent, killed four people at a kosher supermarket before he was shot to death by the police, a video made before the attack surfaced. In that video, Mr. Coulibaly declared his allegiance to the Islamic State, described his role in what he called a coordinated attack to defend Islam, and urged young people to take up the fight.

However, the extent of direct involvement by the Islamic State in the Paris attacks has not been determined. Lone-wolf individuals can declare allegiance to an extremist group such as the Islamic State, and extremist groups can exploit attacks for their propaganda value.

In the case of the Paris attacks, the two brothers who attacked Charlie Hebdo said they were followers of a rival militant group, Al Qaeda in Yemen, also known as Al Qaeda in the Arabian Peninsula. Both extremist groups praised those behind the attacks.

The organizers of the event in Texas contend that they held the event as a celebration of free speech. Pamela Geller, an outspoken blogger who organized the event, has said that Muslims are being singled out as a special group about whom American values of freedom of speech are not being applied.

However, pro-Muslim advocates, while strongly criticizing the violence, have denounced what they see as a provocation that offended many Muslims. In most interpretations of Islam, cartoons or visual representations of Muhammad are considered blasphemous.

Mr. Simpson, who attended an Islamic community center in northwest Phoenix, was convicted in 2011 of lying to F.B.I. agents about whether he had made plans to travel to Somalia. He said he had not when, in fact, he had. Federal prosecutors charged that he had aimed to go to engage in violent jihad. But a judge ruled that the government had not been able to prove that part of the charge, and he was sentenced to three years’ probation. (Source: The New York Times)

Story Date: May 6, 2015