The message aired on an Arab satellite channel on Thursday accused Iraqi officials appointed by the US occupying power of being "servants".
During Saddam's rule, the Baath party's anniversary was marked by parades, speeches and songs in praise of the leadership.
But the recently set up US-backed Iraqi Governing Council scrapped the public holiday and prohibited any such events.
The voice on the tape attacked the council, saying it could not serve the Iraqi people.
The voice also denounced "the lies" of US President George W. Bush and British Prime Minister Tony Blair to justify their invasion of Iraq.
"The occupiers have unveiled their intentions to occupy and divide Iraq. All their allegations (concerning weapons of mass destruction) were baseless," said the voice on the tape.
Iraqis watch a broadcast of a taped
message from Hussein
The authenticity of the tape could not be immediately verified but the voice referred to events in Iraq in recent days.
It was the third message believed to be from the toppled Iraqi leader aired on Arab satellite channels in recent weeks.
Saddam's whereabouts have been a mystery since the fall of Baghdad in 9 April to US and British occupation forces.
The voice, which observers familiar with Saddam's voice and speeches said sounded like that of the toppled leader, also praised towns in Iraq where occupying forces have repeatedly come under attack by resistance fighters.
The US military has placed its forces on high alert across the country in fear of more resistance operations to coincide with the anniversary.
US occupation troops are facing
Our correspondent reported that the US headquarters in the Diyala region came under rocket-propelled grenade (RPG) attack.
There were no reported injuries.
An American patrol was also fired at in Baquba but there were no reported casualties.
Iraqi police also detained our correspondent in Ramadi for allegedly provoking violence. Earlier, the Aljazeera crew were detained and questioned after being accused of co-operating in anti-US resistance attacks.
American troops arrested four handicapped Iraqis in the town of Al-Thara, south of Baghdad reportedly on suspicion of being part of the resistance.
Aljazeera's correspondent in Baghdad said on Thursday the arrests were made as US occupation troops launched a search operation in the town.
"The occupation soldiers were looking for resistance fighters and weapons," our correspondent said.
The detentions are likely to anger the local population even further in light of the hard-handed approach being employed by the US occupying power.
Anti-US sentiment in the country has been running high with many Iraqis accusing the occupiers of failing to provide them with basic necessities and services as well as security.