Jordanian militant Abu Musab al-Zarqawi's Tawhid and Jihad group threatened last week to kill the men if the United States did not release all Iraqi detainees by Saturday.
In a video sent to Al-Jazeera and broadcast early Wednesday, the group said it had carried out its threat against one of the men and would kill the other in 24 hours. The video showed three men dressed in black with their faces covered by black masks. One of the Bulgarian hostages, Georgi Lazov, 30, kneeled in front of them, wearing the same bright orange garment that other hostages wore before they were slain.
The announcer said the video showed the hostage's execution. Jihad Ballout, spokesman for Al-Jazeera, said the station had decided not to broadcast the graphic sections of the video. He declined to say how the killing was carried out.
Bulgaria said Lazov and Ivaylo Kepov were kidnapped while traveling from Bulgaria to Mosul in northern Iraq. They were scheduled to be in Mosul on June 29, the last day either man contacted his family.
The two men's wives had made several appeals for the lives of their husbands on al-Jazeera.
Bulgaria, which has a 480-member infantry battalion serving in central Iraq, sent a team of diplomats to Iraq to try to negotiate the men's freedom.
Deputy Foreign Minister Gergana Grancharova said the ministry still had no confirmation of the execution.
The Tawhid and Jihad earlier had claimed responsibility for the beheading of U.S. businessman Nicholas Berg and South Korean translator Kim Sun-il. It was also believed to be behind a series of attacks on police and security forces in Iraq that killed 100 people in the days leading up to the coalition forces' hand over of power to an Iraqi interim government last month.
Meanwhile, an insurgent group holding Egyptian driver Alsayeid Mohammed Alsayeid Algarabawi demanded the Saudi company he worked for pull out of Iraq within 72 hours, Al Jazeera reported. However, the group did not issue a specific threat against the driver.
A video broadcast on Al-Jazeera showed Algarabawi kneeling on the ground in between two armed, masked men. Algarabawi asked the drivers at his company not to go to Iraq, the newscaster said.