"Two of the soldiers of the caliphate executed an attack on an art exhibit in Garland, Texas, and this exhibit was portraying negative pictures of the Prophet Mohammed," the jihadist group said.
"We tell America that what is coming will be even bigger and more bitter, and that you will see the soldiers of the Islamic State do terrible things," the group announced.
It marked the first time the extremist group, which has captured swathes of territory in Syria and Iraq, claimed to have carried out an attack in the US.
Police said two men drove up to the conference centre Sunday in Garland, where the right-wing American Freedom Defense Initiative was organising the controversial cartoon contest, and began shooting at a security guard, who was wounded in the ankle.
Garland police officers then shot and killed both men.
According to US media reports, the two suspected jihadists were Elton Simpson, 31, and Nadir Soofi, 34, who shared an apartment in Phoenix, Arizona.
Simpson was being investigated by the FBI over alleged plans to travel to Somalia to wage holy war, court records show.
Many Muslims find drawings of the prophet to be disrespectful or outright blasphemous, and such cartoons have been cited by Islamists as motivation in previous attacks.
According to court records seen by AFP, Simpson was sentenced to three years' probation in 2011 after FBI agents presented a court with taped conversations between him and an informant discussing travelling to Somalia to join "their brothers" in war.
The prosecution was unable to prove that Simpson had committed a terror-related offense, but did establish he had lied to investigators when he denied having discussed going to Somalia.
The White House said that President Barack Obama had been briefed on the investigation, which Texas police said was ongoing.
"There is no form of expression that justifies an act of violence," White House spokesman Josh Earnest said.
- 'Bad choice' -
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The American Freedom Defense Initiative, a group listed by civil rights watchdog the Southern Poverty Law Center as an anti-Muslim hate group, had organized the event, which drew about 200 people.
At the event, attended by Dutch far-right politician Geert Wilders and AFDI co-founder Pamela Geller, supporters held an exhibition of entries to a competition to draw caricatures of the Prophet Mohammed.
AFDI had offered a $10,000 prize for the winner of the contest, billed a "free speech" event.
The Washington Post reported Tuesday that the winning entry showed a scowling Mohamed wearing a turban and saying "You can't draw me!"
Under the cartoon was the caption, "That's why I draw you."
The paper identified the winner as Bosch Fawstin, a New York native born to Albanian Muslim immigrants.
Commentators were quick to draw parallels to the January mass shooting at the French satirical weekly Charlie Hebdo in Paris that killed 12 people and wounded 11 more.
But the magazine's film critic, Jean-Baptiste Thoret, who only avoided the attack because he had been late for work said "there is absolutely no comparison."
On Twitter, jihadist Abu Hussain Al-Britani, who extremist monitoring group SITE identified as British IS fighter Junaid Hussain, described the gunmen as "two of our brothers."
But Simpson's father Dunston told ABC News that his son, who he said worked in a dentist's office, simply "made a bad choice."
"We are Americans and we believe in America," Dunston Simpson said. "What my son did reflects very badly on my family."
Wilders told AFP in an e-mail that he was concerned he may have been targeted because he, like one of the Charlie Hebdo cartoonists killed in January, is on a hit list circulated by Al-Qaeda supporters.
"I am shocked. I just spoke for half an hour about the cartoons, Islam and freedom of speech and I had just left the premises," he said.
"This is an attack on the liberties of all of us."