The Syria- and Iraq-based Islamic State (IS) said on its official online radio station that "two soldiers of the caliphate" carried out the attack on Sunday in Garland, a suburb of Dallas.
The White House said it was too early to tell if the two gunmen killed in Garland were tied to IS. Spokesman Josh Earnest said many people tried to capitalize on the influence of the group by claiming allegiance when they were not directly affiliated.
"At this point, this is still under investigation by the FBI and other members of the intelligence community to determine any ties or affiliations that these two individuals may have had with ISIL or other terrorist organizations around the world. So it's too early to say at this point," Earnest said.
US officials said separately that investigators did not know whether the group was opportunistically claiming credit when it had little or no direct or indirect involvement.
One US official said investigators believed it was possible, if not likely, that IS played an "inspirational" rather than "operational" role in the attack.
That would mean the shooters may have immersed themselves in items posted online by IS and other groups like al Qaeda in the Arabian Peninsula intended to incite violence but that the group played no role in directing an attack on the Texas event.
US investigators were going through the shooters' computers and communications devices, officials said.
The State Department said on Tuesday it was offering rewards of up to $7 million for information on four key leaders of the group Islamic State of Iraq and the Levant.
'Might have snapped'
Authorities said roommates Elton Simpson and Nadir Soofi of Phoenix were fatally shot by a police officer when they opened fire with assault rifles outside the cartoon exhibit and contest. An unarmed security guard suffered a minor wound.
The Simpson family said in a statement late Monday it was struggling to understand how it happened.
"We are heartbroken and in a state of deep shock as we grieve," it said. "We send our prayers to everyone affected by this act of senseless violence, especially the security guard who was injured in the line of duty."
Court documents showed Simpson had been under federal surveillance since 2006 and was convicted in 2011 of lying to FBI agents about his desire to join violent jihad in Somalia.
"I believe that perhaps he might have just snapped when he heard about the cartoon contest," Kristina Sitton, a Phoenix attorney who defended him in the case, told CNN.
Such portrayals are considered offensive by Muslims.
The shooting in Garland, an ethnic melting pot city of nearly a quarter million people, was an echo of attacks or threats in other Western countries against images depicting the Prophet Mohammad.
In another Dallas suburb, Richardson, police were investigating an attack by two men on a worshipper leaving evening prayers at a mosque on Monday.
"It is too early to say whether this was a hate crime or an attempted robbery," said Richardson Police spokesman Sergeant Kevin Perlich.
The man was treated on the scene for minor injuries.
Police and federal agents had planned security for months ahead of the Garland event, organized by American Freedom Defense Initiative (AFDI), a free-speech organization that the Southern Poverty Law Center has described as a hate group.
