"The judicial court of the Organisation of al-Qaida in Iraq has sentenced to death the diplomatic envoys of the apostate Algerian government," said the internet statement from the group on Tuesday.
"This is the fate of the ambassadors and the envoys of all infidel governments," said the statement, dated 25 July.
Its authenticity could not be immediately verified.
Algeria's Foreign Ministry declined to comment, and a government official said the issue was too sensitive to make a statement about at the moment.
Algerian Foreign Minister Mohamed Bedjaoui said in comments published on Tuesday: "We have always been on the side of the Iraqi people... . For Algerian envoys to be attacked is something that is beyond comprehension."
On Monday Algeria pulled its last diplomatic staff out of its embassy in Baghdad.
The statement, posted on the website said to be used by al-Qaida in Iraq, did not give details about the fate of mission chief, Ali Belaroussi, 62, and attache Azzedine Belkadi, 47, who were kidnapped by armed men on Thursday near their embassy.
The families of Belaroussi and Belkadi on Tuesday appealed in a newspaper to al-Qaida to free their loved ones.
Al-Qaida in Iraq earlier this month reportedly claimed responsibility for the kidnapping and killing of Egyptian mission chief Ihab al-Sharif.