Meanwhile, efforts to draft a new constitution by an Aug. 15 deadline suffered a setback Thursday when Sunni Arab committee members announced they would not participate until the government accepts demands that one Shiite official said are impossible to meet.
Thursday's kidnappings brought to five the number of key diplomats from Islamic countries targeted in Baghdad in less than three weeks in an attempt to undermine the U.S.-supported Iraqi government.
The top Egyptian envoy was reportedly killed after being kidnapped July 2 after stopping to buy a newspaper in west Baghdad, also without security. A few days later, kidnap attempts against two other Muslim diplomats failed.
The chief of Algeria's mission in Iraq, charge d'affaires Ali Belaroussi, 62, and another Algerian diplomat, Azzedine Belkadi, 47, were abducted along with their driver in west Baghdad's upscale Mansour district, police and Algerian officials said.
In other developments:
By Friday, no claim of responsibility had surfaced, Algerian authorities said. They expressed surprise over why the Algerians were captured, saying Algiers has steadfastly refused to take part in the U.S.-led coalition.
A fellow diplomat, Abdelwahab Felahi, told Algerian radio that he was in another car when he saw their brake lights flash and knew there was a problem.
"I wasn't armed, and I couldn't intervene, and in the time it took to warn police in front of the embassy, the kidnappers, diplomats and their vehicle had disappeared," said Felahi, adding he had been scheduled to meet Belaroussi for lunch a half-hour after the time of the kidnapping.