The Islamic State claimed responsibility Tuesday for the thwarted attack outside a prophet Muhammad cartoon contest near Dallas, threatening to carry out “worse and more bitter” violence on American soil.

The authenticity of the claim — announced on a Syria-based radio station operated by the militant group — could not be immediately verified. Sunday’s shootout in Texas represented the first time the Islamic State has announced links to a high-profile attack in the United States.

U.S. officials, speaking on condition of anonymity, suspect that the Islamic State did not direct the attack, but theorize the gunmen were inspired by the terrorist group’s propaganda, which includes an online English-language magazine. In recent months, the FBI has charged several people with alleged attempts to stage attacks in the United States.

White House spokesman Josh Earnest told reporters the investigation was ongoing, and noted it was “too early to say” whether the Islamic State had a guiding hand in the attack.

“Two soldiers … of the caliphate attacked an exhibit in Garland in American Texas, and this exhibit was holding a contest for drawings offensive to the prophet Muhammad,” the militant group said on its al-Bayan radio station, according to the SITE Intelligence Group, which monitors radical factions around the world.

The statement warned that the United States will be targeted by other Islamic State fighters waging attacks that will be “worse and more bitter, and you will see from the soldiers of the Islam State what will hurt you,” the SITE report said.

The claim, however, offered no hints about how the Islamic State purportedly made contact or directed the two attackers from Phoenix in Sunday’s failed assault.

Both were killed after wounding a security guard at the Curtis Culwell Center in Garland, about 20 miles northeast of Dallas. The suspects, identified as Elton Simpson, 30, and his roommate, Nadir Soofi, 34, had traveled from Phoenix to Garland in time for the event dubbed the Muhammad Art Exhibit.

Simpson was a Muslim convert whom the FBI had previously targeted in a terrorism investigation. Court documents show he was born in Illinois and converted to Islam at a young age. The government began investigating him in 2006, recording conversations between him and a paid informant, The Washington Post reported on Monday.

In May 2009, Simpson told an FBI informant: “It’s time to go to Somalia, brother.” He added: “It’s time. I’m tellin’ you, man. We gonna make it to the battlefield. … It’s time to roll,” according to a federal court document.

Simpson was arrested in January 2010 and charged with lying to agents in connection with terrorism. Authorities suspected he was trying to fly to Somalia, but Simpson said he intended to go to South Africa to study Islam.

Following a bench trial, a judge dropped the terrorism allegations, citing insufficient evidence. His charged was reduced to making a false statement to federal officials, and he was sentenced to three years of probation.

William McCants, an expert on Islamic militants, said it remains “a little tricky” to evaluate the extent of possible Islamic State connections to the Texas attack.

“They could have very loose ties to someone via Twitter. It’s tough to know if this is something that someone high up in the leadership reached out and activated them, or if they did it on their own and gave someone in the [Islamic State] media orbit a heads up just beforehand, or if it’s more after the fact,” said McCants, a fellow at the Brookings Institution and head of its Project on U.S. Relations with the Islamic World. “It’s hard to parse.”

Sunday’s show was hosted by the New York-based American Freedom Defense Initiative — which has been labeled an anti-Muslim “hate group” by the Southern Poverty Law Center — featuring cartoon drawings that lampooned the prophet Muhammad.

Pamela Geller, the group’s president, known for inciting conspiracy theories and speaking out against what she calls the “Islamization” of the United States, organized the event. The keynote speaker was Geert Wilders, who has been outspoken against Islam and marked for assassination by al-Qaeda and its allies.

Almost immediately after the shooting, Geller blamed Islamic State supporters for the attack.

“This incident was obviously related to our event, as evidenced by the ISIS supporters on Twitter taking credit for and praising the gunmen,” she told The Washington Post in an e-mail, referring to the Islamic State, also known as ISIS or ISIL. “The Islamic jihadis are determined to suppress our freedom of speech violently. They struck in Paris and Copenhagen recently, and now in Texas.”

At the time, Garland police spokesman Joe Harn said it was unclear whether the shooting was related to the art event.

The winner of the cartoon contest was Bosch Fawstin, a New York native born to Albanian Muslim immigrants. His entry featured a scowling, turbaned Muhammad saying: “You can’t draw me!”

At the bottom of the cartoon he wrote: “That’s why I draw you.”

The Islamic State has claimed responsibility for dozens of major attacks and slayings in Europe, North Africa and elsewhere. In October, a gunman shot and killed a ceremonial guard at a soldiers memorial in the Canadian capital of Ottawa before storming the nearby Parliament building, where he was fatally shot. Some investigators described the attacker as a potential “lone wolf” militant inspired by the Islamic State, but Canadian officials later said there were no credible links to the group.

Michelle Boorstein in Miami and Adam Goldman in Washington contributed to this report.