The abduction appeared to be part of an ongoing attempt by militants to disrupt the rebuilding of Iraq and came two days after the brazen kidnapping of an Italian journalist.
Giuliana Sgrena, a reporter with the communist newspaper Il Manifesto, was bundled into a car by gunmen as she conducted interviews on a Baghdad street in broad daylight.
There have been two separate claims for her abduction.
The first, from a group calling itself the Islamic Jihad Organisation, set a 72-hour deadline for Italy to withdraw its troops from Iraq, but did not threaten to kill Sgrena.
The second, signed by a group calling itself the Jihad Organisation, threatened to kill her by Monday if Italy refused to get out of Iraq.
The Egyptian men were seized as they left their house in the west of the capital for work. All are employed by a unit of the Egyptian telecoms firm Orascom, which has several contracts in Iraq including one to run Iraqi mobile phone operator Iraqna.
A week after historic elections, the result remains unknown. Electoral commissioners issued partial results on Friday but little further information. They hope to complete the process by Thursday.
The count so far puts a religious Shi’ite coalition in the lead by a long way with two-thirds of the vote, based on results from 35% of polling centres.
The coalition is now insisting it should get the prime minister’s job, currently held by Iyad Allawi, a secular Shi’ite whose bloc is in second place with only 18% of the vote.
The Kurds are expected to have a powerful voice in the new 275-seat national assembly and have hinted they want greater self-determination, stoking fears in Turkey that they may seek full independence.