Militants have threatened to kill three Western hostages unless all female Iraqi prisoners are set free.
The three were seized in their Baghdad house earlier this week
The men - Briton Kenneth Bigley, and US colleagues Jack Hensley and Eugene Armstrong - were shown blindfolded in a video broadcast by al-Jazeera TV.
Their captors are reportedly allied to al-Qaeda militant Abu Musab al-Zarqawi.
Later on Saturday, al-Jazeera showed another tape in which unknown militants threatened to kill 10 hostages unless their US-Turkish company left Iraq.
It is not known when the hostages - whose nationality was not immediately known - were seized.
The militants - from a group called the Salafist Brigades of Abu Bakr al-Seddiq - gave the unnamed company three days to withdraw from Iraq.
British Prime Minister Tony Blair said he was doing everything possible to free the Western hostages, ahead of his meeting with Iraqi leader Iyad Allawi on Sunday. The caretaker Iraqi leader is also set to meet US President George W Bush in the coming days.
The US and British hostages face death unless Iraqi women prisoners held in two Iraqi jails are set free within 48 hours, according to a masked militant in the video, which also appeared on a website linked to Islamist causes.
The three men were abducted at dawn on Thursday from a house they shared in the capital.
The footage shows the hostages, sitting or kneeling in front of a masked gunman, give details of who they are.
A masked man then reads a statement.
"God's soldiers from Tawhid and Jihad were able to abduct three infidels of God's enemies in Baghdad - two Americans and a Briton.
"They offer logistic support to American troops in Iraq, as was shown from investigation and the documents seized with them."
The three hostages had been working as engineers for a building firm based in the United Arab Emirates.
All three men's families have appealed for their safe release and the US embassy said it had a team assigned to the case.
Fighters waging a 17-month insurgency in Iraq have kidnapped more than 100 foreigners in an effort to destabilise the interim government and drive foreigners from the country.
Two French journalists were abducted almost a month ago and two female Italian aid workers, along with two of their Iraqi colleagues, were grabbed from their offices on 7 September.
The group said to be holding the hostages, Tawhid and Jihad (Unification and Holy War), wants Iraqi women in prisons at Abu Ghraib, near Baghdad, and Umm Qasr, in the south of the country, to be released.
The US government has said it holds only two women in Iraq - high-level detainees who are understood to have been part of Saddam Hussein's regime.
One of them is Rihab Rashid Taha - the woman known as Dr Germ for her role in developing Iraqi biological weapons, says the BBC's Caroline Hawley in Baghdad.
The other is thought to be Huda Salih Mahdi Ammash, dubbed Mrs Anthrax, who is believed to have played a key role in developing Iraq's biological weapons.
Tawhid and Jihad is allegedly led by Abu Musab al-Zarqawi, an ally of al-Qaeda who the Americans say is behind much of the violence in Iraq.
The US has offered a $25m reward for his capture.