They say there is no indication the three, aged between 30 and 34, have had ties with Islamist armed groups.
Moroccan Communications Minister and government spokesman Nabil bin Abd Allah said on Sunday the three men were born in the north of the country, in the cities of Tangiers and Tetouan.
Jamal Zugam, 30, is an office worker, Muhammad Bekkali, 31, a mechanic and Muhammad Chaui, 34, a factory worker, the minister said in comments published by the official MAP news agency on Sunday. He gave no other details.
Bin Abd Allah told Reuters on Saturday night a Moroccan security team would travel to Spain on Sunday to help with the investigation.
He said the security officials would try to determine whether those arrested were residents of Spain or another European country.
Also on Sunday Spanish authorities announced they had so far been unable to identify a man who appeared on a video claiming responsibility for Madrid's bomb attacks in the name of al-Qaida.
"At the moment we haven't identified the person," Interior Minister Angel Acebes told a news conference on Sunday, adding Spain had consulted with officials in Britain, France and Portugal.
The video tape, found in a rubbish bin near a Madrid mosque late on Saturday, featured a man speaking Arabic who said: "We claim responsibility for what happened in Madrid just two and a half years after the attacks in New York and Washington.
"This is an answer to your cooperation with the Bush criminals and their allies. This is an answer to crimes which you committed in the world, notably in Iraq and Afghanistan, and there will be more, so help us God."
The claim was made in the name of "Al-Qaida's military spokesman in Europe ... Abu Dukhan al-Afghani."
'Anything is possible'
Angel Acebes : "This will be a long
and a meticulous investigation"
Acebes said Spanish authorities were trying to authenticate the tape, but that right now "we are not discarding any possibility".
The government had previously insisted it considered the
Basque separatist group ETA its prime suspect, and on Sunday Foreign Minister Ana Palacio said her country was still investigating the possibility of whether ETA had collaborated with al-Qaida.
"I would say that anything is possible in this dark, dark world
of terrorists," said Palacio when asked on BBC television if the two groups might have "combined" to carry out the attack.
Acebes said five men - three Moroccans and two Indians - being held on suspicion of being connected to an unexploded bomb recovered from the scene of one of the attacks would be detained under a Spanish anti-terrorism law allowing them to be held for a prolonged period. The five were arrested late on Saturday.
Acebes also confirmed Morocco's identification of the Moroccan suspects and named the two Indian suspects as Vinay Kohly and Suresh Kumar. Acebes added three of the detainees had criminal records. "This will be a long and meticulous investigation," Acebes said.