In Riyadh, police helicopters hovered overhead and anti-riot officers set up checkpoints, according to witnesses.
Crowds dispersed quickly after Friday prayers, where clerics urged against public demonstrations.
In the east of the country, about 500 people are reported to have held peaceful demonstrations in the cities of Al Hofuf and Awamiya. And in Al Ahsa, witnesses said several hundred demonstrators gathered after a sermon given by Sheikh Tawfiq al-Amer, a cleric who was arrested earlier this week for calling for a constitutional monarchy.
But there were no reports of unrest in the city of Al Qateef, where police shot and killed three protesters late on Thursday. A small demonstration took place, one witness told AFP news agency, but was closely watched by police.
The Alriyadh newspaper said there was evidence to indicate that the online calls to protest had come from "seditionists" outside Saudi Arabia.
A new Facebook campaign has been launched, calling for nationwide protests on 20 March.