The world's top oil producer has been fighting a wave of attacks over the past two years, which have so far killed 91 foreign nationals and Saudi citizens.
The latest clash killed al-Qaida's top leader in Saudi Arabia, Saleh al-Awfi, in the holy city of Medina on 18 August. Police arrested 13 suspects in raids the same day.
The source said security forces have since arrested an additional 23 suspects in Medina, two in the town of Arar, and one in the capital, Riyadh, bringing to 41 the number of arrests made since the clashes with Saudi forces in Medina and Riyadh.
In June, Saudi officials listed another 36 most wanted men they were hunting. It is not clear whether any of the recently arrested suspects are on that list.
The interior ministry said those arrested were of various nationalities but did not reveal their names, citing "the (national) interest."
Meanwhile, Saudi authorities said they had thwarted attacks, including one in the capital Riyadh, during a series of coordinated operations last week.
"Security forces managed to... prevent vile attacks that were imminent," when they targeted "hideouts" in Riyadh, the holy city of Medina and the northern town of Arar on 18 August, said an interior ministry statement on Friday.
A raid on a Riyadh "hideout of the deviant group" - official terminology for al-Qaida - targeted a group preparing to carry out "an imminent terrorist attack in the city," said the statement read on state television.
Saudi security officials say they
have thwarted an attack
The clashes came days after Western governments warned that fresh terror attacks might be imminent in Saudi Arabia, where suspected al-Qaida members launched a spate of bombings and shootings in May 2003, many targeting Westerners.
The US embassy in Riyadh and its consulates in Jeddah and Dhahran were closed temporarily this month following information about possible strikes against American offices and citizens.
Australia, Britain, Canada and Germany also issued alerts about serious threats against their nationals in Saudi Arabia.
Saudi security forces have launched a relentless crackdown on al-Qaida suspects since the wave of unrest began more than two years ago.