Cairo: The Islamic State claimed responsibility on Tuesday for a weekend attack at a centre near Dallas, Texas, that was exhibiting cartoon depictions of the Prophet Muhammad - though it offered no evidence of a direct link to the attackers.

An audio statement on the extremist group's Al Bayan radio station said that "two soldiers of the caliphate" carried out Sunday's attack and promised the group would deliver more attacks in the future.

The Islamic State did not provide details and it was unclear whether the group was opportunistically claiming the attack as its own. It was the first time the IS, which frequently calls for attacks against the West, had claimed responsibility for one in the United States.

Two suspects in Sunday's attack in the Dallas suburb of Garland were shot dead after opening fire at a security guard outside the centre.

It was also unclear from the statement whether the group, which has captured large swaths of territory in Syria and Iraq, had an actual hand in the operation, or whether the two suspects had pledged allegiance to the group and then carried out the attack on their own.

The suspects have been identified by officials as Elton Simpson and Nadir Soofi. They opened fire on an unarmed security officer stationed outside the contest centre featuring cartoons of the Prophet Muhammad.

According to mainstream Islamic tradition, any physical depiction of the Prophet Muhammad and others prophets, including Jesus and Moses - even a respectful one - is considered blasphemous. Drawings similar to those featured at the Texas event have sparked violence around the world.

The authenticity of the IS statement could not be independently confirmed but it was read on the Al Bayan radio - a station based in the Syrian city of Raqqa, which the group has proclaimed the capital of its self-styled caliphate.

"We tell... America that what is coming will be more grievous and more bitter and you will see from the soldiers of the Caliphate what will harm you, God willing," it said.

There have been numerous attacks in Western countries believed related in some way to the group, which holds roughly a third of Iraq and Syria.

In October, Canada was hit by two terror attacks by the so-called "lone wolves" believed to have been inspired by the Islamic State group. In Ottawa, a gunman shot and killed a soldier at Canada's National War Memorial and then stormed parliament before being gunned down. Two days earlier, a man ran over two soldiers in a parking lot in Quebec, killing one and injuring the other before being shot to death by police.

Following the IS claim of responsibility, IS members and followers celebrated online with postings on IS-affiliated militant websites.

"How are you (Americans) going to live when we create our lone wolves to be nuclear bombs... by God, you can't match us and in the heart of your homes you will see," said one Twitter posting.

"Let anyone who wants to draw the picture of our Prophet to think one thousand times before doing so, because our hands can reach his neck," said another.