The kidnappers have sent the videotape to media outlets, reports CBS News Correspondent Elaine Cobbe. The tape shows one of the men, an Indian, with a gun pointed to his head. He was wearing an orange garment similar to ones worn by previous foreign hostages that were killed.
The group, calling itself "The Holders of the Black Banner" said last week it had kidnapped three Kenyans, three Indians and an Egyptian and would begin beheading them last Saturday if the truck drivers' Kuwaiti employer did not cease business in Iraq and the hostages' countries did not withdraw all their citizens from Iraq.
In other videos, the kidnappers added to their demands, but also appeared to extend the deadline.
Meanwhile, a national conference considered a crucial first step in the country's fledgling move toward democracy was postponed for two weeks, an organizer said Thursday. The announcement came a day after a massive car bombing that killed 70 people.
The conference had been due to start Saturday. But it has been plagued by difficulties before it even began.
Key political groups have been promising to boycott, leaders in ethnically diverse areas have been unable to agree on delegates to send — and even before Wednesday's car bombing, officials have expressed worries the gathering will be a target for terror attacks.
In other developments:
The gunman in the video Thursday said that no one had contacted the group so it would kill one of the hostages at 7 p.m. Friday because they will be considered "fighters who have supported the infidel occupier by transporting their supplies."
The group did not specify which hostage it would kill.
The gunman said the truckers' governments had ignored the threat against the men, and he scolded the Egyptian government for working for the release of an Egyptian diplomat seized last week and freed Monday, but doing little for the Egyptian driver.
Egyptian diplomats in Baghdad declined to comment. All three nations have made repeated appeals to the kidnappers to free their citizens.
The men all worked as truck drivers for Kuwait & Gulf Link Transport Co., which said it would take "all necessary measures" to save their lives. However, it said it would not pull out of Iraq, reports Cobbe.
The hostages were identified as Ibrahim Khamis, Salm Faiz Khamis and Jalal Awadh, of Kenya; Antaryami, Tilak Raj and Sukdev Singh, of India; and Mohammed Ali Sanad, of Egypt.
More than 70 foreigners have been taken hostage in Iraq in recent months in an effort by insurgents to force foreign troops out of the country and to deter truck drivers and other workers involved in trade and reconstruction from coming.
The threat Thursday came just hours after an insurgent group linked to Jordanian militant Abu Musab al-Zarqawi said it had kidnapped a Somali truck driver and threatened to behead him if his Kuwaiti company didn't stop working here.
On Wednesday night, another militant group that it had killed two Pakistani hostages.
Abdul Halim al-Ruhaimi, one of the national conference's organizers, said that after U.N. requests, the Iraqis agreed to a postponement until mid-August to give officials time to speak with groups that had been reluctant to attend.
U.N. officials told The Associated Press they had repeatedly called on organizers to delay the conference for as long as a month to encourage wider participation and ensure it was properly prepared.
Al-Ruhaimi denied the suicide attack had any role in the decision to postpone the conference, which is to select a national assembly that will have some semi-parliamentary powers.
But the delay highlighted how Iraq's new government has struggled to get momentum in the democratic process even as violence has shown no sign of easing.