The Islamic State group claimed responsibility on Tuesday for the assault on a Texas cartoon contest that featured images of the Prophet Muhammad. But counterterrorism experts said IS has a history of asserting involvement in attacks in which it had no operational role.

That suggests the two gunmen could have carried out their own lone-wolf-style strike before they were shot dead at the scene of Sunday's shooting in the Dallas suburb of Garland.

The evidence does not indicate the attack was directed by the Islamic State, "but rather inspired by them", said Republican Michael McCaul, chairman of the House Homeland Security Committee, who was briefed on the investigation by federal law enforcement officials. "This is the textbook case of what we're most concerned about."

Federal officials identified the pair as Elton Simpson and Nadir Soofi, both US citizens who lived in Phoenix. Federal authorities had been scrutinizing Simpson's social media presence recently but had no indication he was plotting an attack, said one federal official familiar with the investigation.

A Twitter account linked to Simpson included images of Anwar al-Awlaki, a radical cleric killed in a CIA drone strike in Yemen. Al-Awlaki was born in the US.

Among the hashtags used by the account was "(hash) texasattack". And one of the final tweets was, "May Allah accept us as mujahedeen", or holy warriors.

"Was he on the radar? Sure he was," McCaul said from Turkey, where he was leading a congressional delegation.

A federal law enforcement official said authorities had an open investigation into Simpson at the time of the shootings.

The official, who was not authorized to discuss the ongoing investigation and spoke on condition of anonymity, also said investigators will be studying the contacts the men had before the shootings, both with associates in the US and abroad, to determine any additional terror-related ties.

Texas has more people associated with Muslim congregations, about 422,000, or 1.7 percent of its population, than any other US state.