ISIS has claimed responsibility for the shooting at a Prophet Muhammad cartoon contest in Garland, Texas on Sunday.

The militant group described the two gunmen as "soldiers of the caliphate" in a message broadcast on its radio station.

The gunmen, who were shot dead after opening fire outside the event, have been identified as roommates Elton Simpson and Nadir Soofi, from Phoenix, Arizona

Federal agents have been monitoring Simpson for a number of years, according to reports by Reuters. Court documents show Simpson had been under surveillance since 2006 and was convicted in 2011 of lying to FBI agents over his desire to join violent jihad in Somalia.

The shooting in the Dallas suburb was an echo of attacks or threats in other Western countries against images depicting the Prophet Mohammad. In January, gunmen killed 12 people in the Paris offices of French satirical magazine Charlie Hebdo in what was said to be revenge for its cartoons.

Support on social media had suggested a link between ISIS and Sunday's attack, but the radio statement was the first official claim of the group's involvement. If true, it is believed to be the first Islamic State attack on US soil.

"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 statement on Idha'at al-Bayan – the group's radio station – said.

The Texas incident unfolded on Sunday when a car drove up behind an indoor arena in Garland, where 200 people were attending the Muhammad Art Exhibit and Contest. Many Muslims consider such depictions of Muhammad to be offensive.

Two men jumped from the car and fired at a police car that was blocking an arena parking lot entrance. A Garland police officer and an unarmed security guard were in the squad car and began to exit as the vehicle approached. The gunmen wounded the security guard, and the police officer returned fire, killing both assailants.

The Times reports that shortly before the gunmen fired the first shots, a tweet was sent from a Twitter account with the name Sharia is Light saying "May Allah accept us as mujahideen ... #texasattack."

The tweet also said: "My bro and myself have given bay'ah to Amirul ­Mu'mineen," which is understood to be a sign of allegiance to ISIS leader Abu Bakr al-Baghdadi.

Those inside the Curtis Culwell Center, who had gone through heavy security to enter the event, were not aware of the attack until afterward.

"At this point it does seem clear that an officer of the Garland Police Department acted quickly and decisively and thereby likely saved a number of innocent lives," US Homeland Security Secretary Jeh Johnson said in a statement.

Police and federal agents had planned security for months ahead of the event, organised by American Freedom Defense Initiative (AFDI), a free-speech organisation that the Southern Poverty Law Center has described as a hate group, and which paid $10,000 for extra protection.

The contest offered a $10,000 prize for the best artwork or cartoon depicting the Prophet. Artist Bosch Fawstin won for a depiction of a sword-wielding Prophet in a turban shouting, "You can't draw me."

The shooters wore protective gear and had extra ammunition in their car, Garland police spokesman Joe Harn said. Police feared there may have been explosives in the vehicle, but no bomb was found.

"Obviously they were there to shoot people," Harn said at a news conference.

A bomb squad, the Federal Bureau of Investigation, a SWAT team and the US Bureau of Alcohol, Tobacco, Firearms and Explosives had been involved in preparations for security around the exhibit, Garland police said.

In Phoenix, policed searched the men's apartment and a white van parked outside, with its side windows broken.

Simpson was charged in 2010 with lying to FBI officials over discussions he had with an informant about his desire to travel to Somalia to engage in violent jihad and waived his right to a jury trial.

US District Judge Mary Murguia in 2011 found him guilty of making a false statement. She found insufficient evidence to conclude the false statement involved international terrorism.

Simpson was sentenced to three years probation and ordered to pay $600 in fines and penalties.

The court documents say federal authorities began monitoring Simpson in 2006 because he was associated with an individual the FBI believed was trying to set up a terrorist cell in Arizona.

At one point, according to the documents, the FBI tried "unsuccessfully" to put Simpson on a US government no-fly list.

Simpson's father told ABC News his son was "always a good kid" but said they had "some very serious differences". "We are Americans and we believe in America," Dunston Simpson told ABC News. "What my son did reflects very badly on my family."

Additional reporting by Reuters.