(Adds comments from Robert Spencer of Jihad Watch, paragraphs 3-5)
By Mark Hosenball and Ian Simpson
WASHINGTON, May 5 (Reuters) - U.S. investigators were investigating a claim by Islamic State that it was behind a failed attack on a Texas exhibit of cartoons of the Prophet Mohammad in which two gunmen were killed, but officials said on Tuesday they doubted the militant group's direct involvement.
The Syria- and Iraq-based Islamic State 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.
As the U.S. government sought to verify the Islamic State connection, a co-sponsor of the event that was attacked by the two Arizona men said the attempt to disrupt the controversial drawing contest motivated him to hold another one.
Robert Spencer, who runs the website Jihad Watch, said that a few days before the cartoon contest, the FBI showed him two Twitter messages that threatened violence at the event.
"We kind of have to do it again," Spencer told Reuters by telephone. He said that not doing so would amount to giving militants the power to censor.
The White House said it was too early to tell whether the two gunmen were tied to Islamic State, which has taken control of parts of Iraq and Syria in the past year and has sympathizers in several countries.
White House spokesman Josh Earnest said many people tried to capitalize on the influence of the group by claiming allegiance when they were not directly affiliated.
"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, using an alternative acronym for the group.
U.S. 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 U.S. 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 gunmen may have immersed themselves in items posted online by Islamic State and other groups such as 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.
U.S. 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 leaders of Islamic State.
"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 event. 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.
Police and federal agents had planned security for months before the event, which was organized by American Freedom Defense Initiative (AFDI), a free-speech organization that the Southern Poverty Law Center has described as a hate group.
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. (Additional reporting by Ahmed Tolba in Cairo, Katharine Houreld in Islamabad, David Schwartz in Phoenix, Arizona, and Julia Edwards in Washington; Writing by Jon Herskovitz; Editing by Ted Botha, Alden Bentley, Grant McCool)