The Islamic State group proclaimed early on Tuesday that it had carried out its first terrorist attack on American soil and warned of "bigger and more bitter" strikes to come as it took responsibility for the failed assault on an art contest featuring cartoons of the Prophet Muhammad held in Texas at the weekend.

Isis broadcast a statement on its al-Bayan radio station declaring that "two soldiers of the caliphate" carried out Sunday's attack in Garland, near Dallas, Texas, where two gunmen were shot dead as they apparently attempted to storm the art show.

It is still not clear if the two gunmen - identified by officials as Elton Simpson and Nadir Soofi, roommates in an apartment complex in Phoenix, Arizona - were actually connected with the group, whether they devised their own attack inspired by Isis, or neither.

US authorities have said they are investigating whether Sunday's shooting had any link to international terrorism.