Speaking at a news conference, Nayef provided details of the arrests he announced the previous day as having taken place in the holy city of Medina, western Saudi Arabia, during the past few days.
The detainees included three wanted clerics — Ali al-Khudair, Ahmad al-Khalidi and Nasser al-Fahd — the minister said late Wednesday in Tabuk, 60 miles south of the Jordanian-Saudi border.
The clerics had urged people to support the 19 militants wanted in connection with a weapons cache found May 6 near the site of the Riyadh attacks six days later.
The clerics described the 19 suspects as "some of the best mujahedeen (holy warriors) and virtuous devout men … who have offered their lives, money and blood to God almighty and fought the spiteful Crusaders in Afghanistan with heroism" in a statement posted on the Internet.
The clerics, who had been in hiding for some time, are known to back al Qaeda, the terror group led by Osama bin Laden that is suspected of instigating the Riyadh attacks as well as those of Sept. 11, 2001, on the United States.
In the Riyadh attacks, the suicide assailants detonated vehicle bombs in housing compounds for foreigners in the Saudi capital, killing 25 bystanders, including eight Americans.
Nayef was dismissive of the clerics, telling reporters: "Those who claim to be clerics and issue religious edicts are far from that. In reality, they are worthless."
The prince said that in one case, police detained a suspect who was fleeing Medina in a car.
"He was arrested on the road to Mecca with three women who seem to be wives of some of (the militants)," Nayef said, according to Al-Riyadh newspaper. It was not clear if the women, who are not Saudis, have been detained as well.
Nayef said police had identified six of the nine bodies of the Riyadh suicide bombers. Four of the six were among the 19 men wanted for the weapons cache, the minister added.
Saudi papers reported Wednesday that officials had arrested five people in Medina, including Ali Abd al-Rahman al-Faqasi al-Ghamdi, whom U.S. officials believe to be one of al Qaeda's top figures in Saudi Arabia.
Al-Ghamdi is suspected of masterminding the Riyadh attacks.
Saudi officials have detained about 100 people since the Riyadh bombings. Last week, reports indicated that three of those arrested were planning a 9/11-style hijacking in Jeddah.
The bombings in Riyadh prompted stricter security and the closing of the U.S. Embassy there. But the American mission re-opened on Sunday, and has apparently operated normally since then.
In other developments in the campaign against terrorist groups:
Staffers at the paper said Al-Watan's manager fired Khashoggi but that the decision came from the Information Ministry. Under Saudi press laws, the government approves the hiring and firing of newspaper editors. Newspapers are privately owned but government guided.
The group is a Palestinian support organization that helps fund suicide bombings and other attacks in Israel, the West Bank and Gaza strip, said terrorism expert Paul Wilkinson, chairman of the Center for the Study of Terrorism and Political Violence at St. Andrews University.
The widening crackdown on the Umm Al Qura group follows the arrests Sunday of its acting chief, who is an Egyptian, and two other Thai members on charges of international terrorism and links to Jemaah Islamiyah. They face up to life in prison if convicted.