Texas police shot dead two gunmen who opened fire on Sunday outside an exhibit of caricatures of the Prophet Mohammad that was organised by a group described as anti-Islamic and billed as a free-speech event.

Citing a senior FBI official, ABC News identified one of the gunmen as Elton Simpson, an Arizona man who was the target of a terror investigation. FBI agents and a bomb squad were searching Simpson's Phoenix home, ABC said.

Phoenix's KPHO TV reported that the second man lived in the same apartment complex as Simpson, the Autumn Ridge Apartments. He was not identified, and the second man’s apartment was searched, the station said, quoting an FBI agent.

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

The attack on Sunday took place at about 7:00pm local time in a parking lot of the Curtis Culwell Center, an indoor arena in Carland, northeast of Dallas. Geert Wilders, a polarizing Dutch politician and anti-Islamic campaigner who is on an al-Qaeda hit list, was among the speakers at the event.

Garland police and the FBI had no immediate comment on the report.