WASHINGTON (AFP) - The White House said Tuesday it was too soon to tell if ISIS (Islamic State in Iraq and Syria) was behind an attack in Texas targeting an exhibit of caricatures of the Prophet Muhammad, despite claims by the extremists.

The ISIS group earlier claimed responsibility for Sunday's attack, in which two gunmen shot a security guard in a Dallas suburb before being killed by a police officer outside an event showcasing the cartoons, which many Muslims find offensive.

The case "is still under investigation by the FBI and other members of the intelligence community" to determine if the two assailants had any ties to ISIS, White House spokesman Josh Earnest told reporters. "So it's too early to say at this point."

The ISIS claim marked the first time the extremist group, which has captured swathes of territory in Syria and Iraq using brutal methods, alleged to have carried out an attack in the United States.

"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 Muhammad," the extremist group said.

But Earnest said ISIS and other extremists are often "trying to capitalise on the opportunity that's presented by social media to try to communicate with individuals around the world, including inside the United States".

Police said the two gunmen drove up to the conference centre on Sunday in Garland, where the right-wing American Freedom Defence Initiative was organising a controversial Muhammad cartoon contest, and opened fire with assault rifles, hitting a security guard in the ankle.

A Garland police officer then shot and killed both men with his service pistol.

The two suspected extremists were Elton Simpson, 31, and Nadir Soofi, 34, who shared an apartment in Phoenix, Arizona.

A Twitter account suspected of being linked to the gunmen vowed allegiance to the head of the ISIS group, Abu Bakr al-Baghdadi, the New York Times reported. But ISIS released no "martyr" video and authorities had yet to find evidence of a direct connection to the extremists.

A day after FBI agents searched the apartment where the two men had lived, a portrait of Simpson began to take shape, as acquaintances recalled his passion for basketball and his youthful conversion to Islam.

But there were scant details available about Soofi, except that he had owned a struggling pizza and hot wings restaurant. Managing his business reportedly meant he sometimes had to skip prayers at the mosque.

Soofi reportedly graduated from the International School of Islamabad, in Pakistan, in 1998, and attended the University of Utah. A cousin told local media Soofi was born in the United States.

Simpson was convicted in 2011 of lying to the FBI about his plans to travel to Somalia. Federal prosecutors accused him of wanting to wage "violent jihad" there but a judge found the government had failed to prove that charge. Simpson was sentenced to three years' probation.

But the FBI reportedly started investigating Simpson again in recent months after he began posting about ISIS on social media.

Simpson's online activity was monitored and he was placed under occasional surveillance, though the authorities saw no sign that he planned to stage an attack, according to media reports.

Kristina Sitton, a Phoenix attorney who represented Simpson in his court case, said she could not imagine why Simpson had turned to violence.

"I can only think that he must have snapped at the event that was taking place there," she said.

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.

The American Freedom Defence Initiative, a group listed by civil rights watchdog the Southern Poverty Law Centre as an anti-Muslim hate group, had organised the event, which drew about 200 people.

Commentators have drawn parallels to the January mass shooting at the French satirical weekly Charlie Hebdo in Paris that killed 12 people and wounded 11 more.

In the Pakistani city of Peshawar, a crowd of about 70 people offered prayers for Soofi and praised him for his actions.

"I don't know Nadir Soofi, I have never met him in my life but I praise him, he is a martyr and a real hero of Islam who gave his life while defending the honour of the holy prophet in the land of infidels," Pir Muhammad Chishti, the cleric who organised the gathering, said.