The Muslims were preparing a Sunday Sedeqa, a religious program of food and drinks at all mosques in the capital.
After night attacks, the mosques sent out distress calls to which hundreds of Muslims responded by rushing towards the mosques.
In the ensuing clashes, police killed at least four Muslims and arrested dozens, a source said.
The deaths have not been confirmed by an independent source.
Those who suffered police attacks and teargas received treatments at hospitals. Also on Friday night,gunfire broke out near Efoita Mosque in Kolfe district in the capital, while the city plunged into darkness as more Muslims poured into the streets in response to calls for help.
Millions of Ethiopian Muslims have been peacefully demanding for nearly one year that the government remove the un-elected Majlis (governing council) as well as stop the state-sponsored imposition of a new Lebanon-imported religion called Ahbash.
The government of Prime Minister Meles Zenawi has been labeling the demands of the Ethiopian Muslims as the demands of religious extremists. So far, the Muslims have remained law-abiding, informing the public to respect the constitution and avoid any violence.
Ealier Saturday morning, thousands of Ethiopian Muslims were seen heading toward the grand Anwar Mosque in repsonse to unusual distress calls that were sent out Friday night. Observers say tension is very likely to deepen unless the Meles Zenawi regime desists from falsifying the nature of the Muslim demands.
Observers also reported that the Muslims who were fleeing police attacks in the night were sheltered and those who suffered teargas injuries treated by their Christian friends.