The taped message was broadcast by al-Arabiya television network on Sunday.
The spokesman, Abu Abd al-Rahman al-Najdi, claimed to be a member of al-Qaida and said the organisation was not involved in car bombings which killed prominent Shia cleric Ayat Allah Muhammad Baqir al-Hakim and 82 others.
Western diplomats and Iraqi Shia leaders had attributed the attacks to al-Qaida within hours of the explosion outside the Imam Ali Mosque on 29 August.
The lethal bombing led to various armed groups taking security into their own hands.
But US-led occupation forces set a 13 September deadline for their disarmament, a military spokesman said on Sunday.
"After that, we will take their arms away and, if they resist, we will arrest them and put them in jail," said Captain Edward Lofland, spokesman for the US Marines in Najaf.
Lofland said the occupation coalition had asked the US-appointed Iraqi interim Governing Council to appeal to the various militia groups running the city to disarm voluntarily before the deadline.
But Shia cleric Muqtada al-Sadr's armed militia has already said it would not lay down its weapons, a statement repeated by the cleric's office on Sunday.
Deadline to withdraw
However, a minister in Iraq's interim government said on Sunday he wanted to see US and British soldiers pull out of major cities within six months.
Iraq's new electricity minister, Ayham al-Samarrai, told the BBC that occupation forces should shrink away into the countryside by the beginning of next year and let the Iraqi army take over in urban areas.
"I am looking to see everybody going out of the cities in a very short time," al-Samarrai said in an interview with BBC television.
Referring to the Iraqi army, he said: "I think we are already in the process of putting that army together."