South African police hunting for three men who stabbed worshippers at a mosque outside Durban said on Friday that the attackers' motive was unknown but "elements of extremism" were involved.

Three attackers killed one worshipper, reported to be an imam, and seriously injured two others after midday prayers on Thursday at a mosque in Verulam town, on the outskirts of the eastern port city.

The assailants, who also set off a petrol bomb inside the Shia mosque, escaped in a car after the attack.

"There are elements of extremism because the incident happened in a place of worship and the manner in which it was conducted," Simphiwe Mhlongo, spokesman for the Hawks police unit, told AFP.

"It shows hatred towards the worshippers."

Mhlongo stressed that the motive for the attack was still unknown, adding that a major hunt was under way to find the attackers.

"The whole law enforcement forces are out, including private security, local detectives and police. Everyone is out on the lookout for the suspects," he said.

The man killed had his throat slit, and the other two injured men were stabbed — one in the abdomen and the other in the groin of his left leg, according to medics at the scene.

The blood-soaked victims were found lying in the forecourt of the mosque by emergency services.

One man who was attacked inside the building jumped out of a window when it was set alight by the petrol bomb.

A knife was left on the ground, but police declined to confirm earlier reports that the attackers had carried guns.

The incident appeared to be unprecedented in South Africa, where about 1.5 percent of the country's 55 million population is Muslim.

The country prides itself on religious tolerance and has little record of violence related to religion.

The South African parliament's police committee condemned the attack.

"A mosque is a religious institution, and South Africa's constitution guarantees and protects the right to religious practices," its chairman Francois Beukman said.

"We want our communities to live in harmony, practising their religions without fear."