"The head of the Algerian mission Ali Belaroussi and the diplomat Azzedine Belkadi, whose government is ruling in violation of God's will, were killed," said the written statement on Wednesday, which could not be independently verified.
Belaroussi and Belkadi were kidnapped at gunpoint last Thursday in Baghdad's upscale Mansour area.
The pair appeared in a video made public on Tuesday blindfolded and in captivity, giving their names and home addresses.
It was the first time they had been seen since being abducted.
Wednesday's statement, which appeared on a website, claimed the envoys had been killed because of the Algerian government's repression of Muslims in their North African country.
Al-Qaida blames Algeria
"We won't forget what Algeria did to Muslims, by killings, destruction and spilling their blood," said the statement.
Al-Qaida in Iraq, the group led by Jordanian Abu Musab al-Zarqawi, has claimed responsibility for attacking three other diplomats from Muslim nations.
Egyptian envoy Ihab al-Sherif, 51, was seized on 2 July in Iraq as part of an apparent campaign to undermine Arab nations' support for the Iraqi government.
Azzedine Belkadi appeared in a
video made public on Tuesday
Al-Qaida in Iraq later claimed al-Sherif had been killed, but provided no evidence and his body has not been found.
After al-Sherif's kidnapping, attackers in Iraq fired on envoys from Pakistan and Bahrain in what police said were kidnap attempts.
The Pakistani escaped unharmed, and the Bahraini envoy was slightly wounded.