The White House says it's too early to link the Islamic State group to an attack in Texas targeting an exhibit of caricatures of the Prophet Mohammed organised by an anti-Muslim right-wing group.

White House spokesman Josh Earnest said on Tuesday that the attack by two gunmen was "still under investigation," adding it's "too early to say at this point" whether Islamic State fighters were responsible.

"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 organisations around the world," Earnest said.

The Islamic State group had earlier in the day claimed responsibility for the attack, saying "two of the soldiers of the caliphate" had carried it out.

Earnest cautioned that extremists sometimes make claims of responsibility for propaganda purposes "to try to communicate with individuals around the world, including inside the United States."