An Aljazeera producer said on Tuesday the kidnappers threatened to kill the hostages, Thomas Nitzschke and Rene Braeunlich, if their demands were not met within 72 hours.
The tape arrived on Tuesday. The producer spoke on condition of anonymity because he was not authorised to answer inquiries.
The brief tape showed Nitzschke and Braeunlich, both engineers, seated on the floor in front of a group of armed men.
Aljazeera said the previously unknown group, the Tawhid and Sunnah Brigade, demanded that the German government should close its embassy in Baghdad, withdraw all German companies from Iraq and stop co-operation with the Iraqi government.
The last tape aired showing the Germans appeared on 27 January on Aljazeera and was dated 24 January, the day they were abducted in the northern industrial city of Beiji.
German Chancellor Angela Merkel had condemned "this cruel kidnapping" and had called for their release "without delay."
The engineers, who work for a company in Leipzig, were kidnapped only two days after arriving in Iraq by armed men wearing military fatigues.
At least five foreigners were kidnapped in January: the Germans, two Kenyan engineers and American journalist Jill Carroll.
"[Germany condemns] this cruel kidnapping and calls for their release without delay"
In other news, a British soldier was killed in an explosion in Iraq on Tuesday, the 100th British service member to die since the 2003 invasion, the UK Ministry of Defence said.
Three other soldiers were injured in the blast - one seriously - near the Ten Platforms Port in Umm Qasr, which is south of the city of Basra near the Kuwait border, the ministry said.
Corporal Gordon Alexander Pritchard, 31, who was leading a three-vehicle convoy, died when they were hit by the blast.
On Monday, another British soldier from the 7th Armoured Brigade who served with 1st Battalion of the Highlanders regiment died after being shot on patrol in the southern Maysan province.
The family of Lance Corporal Allan Douglas said the 22-year-old was on his first tour of duty in Iraq and had been in the country for only seven weeks.
Tony Blair, the British prime minister, vowed on Tuesday to see the job through in Iraq. "It's a tragedy when we lose any soldier," he said in an interview with BBC television. "But we have to understand why it's important that we see this through."
Blair added: "It is important because what is happening in Afghanistan and Iraq is that the people of those countries want to leave behind terrorism and extremism and they want to embrace democracy."
At least 100 British soldiers have
been killed in Iraq
Meanwhile, the Iraqi army has taken control from the US military of a central Baghdad base responsible for providing security to Iraqi government buildings, the US command said in a statement on Tuesday.
The US 4th Infantry Division's 4th Brigade Combat Team officially transferred authority of the base, located in the heavily fortified Green Zone, to the Iraqi army's 5th Brigade, 6th Division.
The handover was the latest by the US as part of a programme to transfer responsibility to Iraq's so that the US can draw down its forces in Iraq.
Council set up
On the political front, Aljazeera reports that the Sunni-dominated Iraqi Accord Front, led by Adnan al-Dulaimi, and the secular Iraqi National List, led by Iyad Allawi, have decided to set up a body called The Joint Council for National Work, comprising 60 deputies, to conduct negotiations on the formation of a new government.
The leaders said the council would seek to co-ordinate the positions of different political organisations, and would welcome any other political factions wishing to join it.