The group, known by its French acronym GICM, is considered a terrorist group by several governments and has been implicated in the Madrid and Casablanca attacks.
Experts say the GICM was started by Moroccans who had traveled to Afghanistan in the 1990s.
Moroccan authorities released few details about Houssaini's suspected wrongdoing, but experts have described him as a key figure in the May 2003 attacks on Casablanca, which killed 45 people.
Moroccan suspicions
Jean-Charles Brisard, a French private investigator who studies the GICM, and Moroccan media have said Houssaini is suspected by Moroccan authorities of having made the explosives used in the Casablanca bombings.
Houssaini was born in Meknes and studied chemistry before traveling to Afghanistan, where he allegedly helped found the GICM and taught bomb-making in Kabul in 2000, Brisard said.
Brisard said that, immediately after the Casablanca attacks, Houssaini allegedly decamped to Iraq, likely with help from a terrorist cell in Germany supporting Abu-Musab al-Zarqawi.
Al-Zarqawi, a Jordanian, went on to become chief of al-Qaeda in Iraq before he was killed by US forces in June 2006.'
Doubts remain
However although Houssaini has been linked the group thought to be behind the Casablanca attacks, it is not known it was personally involved in the bombings themselves.
Achour said the investigation of Houssaini has not linked him personally to either the Casablanca or Madrid bombings.
Spain's National Court and Spanish police said on Friday that Houssaini is not wanted in the Madrid attacks.
They said his name has come up in the Spanish investigation but only in connection to the Casablanca bombings.