Assistant Interior Minister Major General Hussein Ali Kamal told Aljazeera on Monday that the two were detained over the Baghdad abductions.
Also on Monday, the group led by al-Qaida's frontman in Iraq, Abu Musab al-Zarqawi, posted on a website pictures of identity papers apparently belonging to one of the two Algerian diplomats kidnapped in Iraq.
A membership card of the Iraqi Hunting Club bearing the name of Ali Belaroussi written in Arabic was shown on a website.
The document's authenticity could not be verified.
Armed men seized Algeria's charge d'affaires, Belaroussi, and his colleague Ezzedin Ben Kadi as they were leaving their embassy by car last week.
Al-Zarqawi loyalists claimed responsibility for the kidnappings in an internet statement on Saturday.
Algeria on Monday recalled its last diplomat from Iraq, the APS news agency reported.
Citing unspecified sources, the agency said the wife of Belaroussi also had been repatriated.
Algeria's last diplomat in Baghdad, Bachir Belhadj, and Belaroussi's wife "arrived in Amman before continuing their trip to Algiers", the source said.
Algerian Foreign Minister Mohamed Bedjaoui said the Algerian government was working hard to have the two diplomats freed.
Diplomatic attache Ezzedin Ben
Kadi also was seized
"The government is not sitting idle. I cannot tell you what it is doing right now, but it is doing everything it can for the two nationals to be freed," he said on state radio from a visit to London.
"We have always sided with the Iraqi people, we have always fought for its sovereignty," said the minister, adding: "We don't understand. That anybody would attack Algerian nationals is something that is absolutely beyond understanding."
The abduction was the second high-profile kidnapping this month after Egypt's top envoy Ihab al-Sharif was seized by armed men on 2 July in Baghdad.
Al-Zarqawi's group claimed his abduction and later his murder, labeling him "the ambassador of the infidels" and citing a previous diplomatic posting in Israel.