The other victims were in critical condition after the attack in the eastern town of Verulam, just north of the city of Durban, South Africa's state broadcaster SABC reported.
Taliep said the council called on the police and other government structures to ensure the necessary criminal investigations are done so "the perpetrators and criminals can be brought to book and face the full might of the law".
It was too early to comment on the circumstances of the attack, said Nick Piper, a director at Signal Risk, an Africa-focused risk management firm.
"The local people here identified them", Balram said.
The attack on a mosque in Verulam, KwaZulu-Natal, should not be assumed to be part of sectarian violence.
He condemned the incident and said there is no need for sectarianism or use of violence.
"Before the assailants left the mosque, a petrol bomb was thrown into the mosque and it was set alight".
About 1.5 percent of the country's 55 million population is Muslim. One of the attack victims jumped from a side window of the smoking building.
"We reiterate and emphasise the core Islamic teaching and principle of "respect for all human beings", Shaykh Isgaak Taliep, secretary general of the Muslim Judicial Council, said.
He said that witnesses told officers that three men‚ who were armed with knives and guns‚ "attacked the mosque‚ slitting the victims' throats and then set fire to the building".
"It is the first time anything like this has happened in South Africa, let alone in KwaZulu-Natal province", Faizel Suliman, chairman of the SA Muslim Network, told AFP.
"A mosque is a religious institution and South Africa's Constitution guarantees and protects the right to religious practices", said chairperson of the committee Francois Beukman.
"It was a sudden attack and at this point we don't have enough information".