The imam's name was not known but he called on protesters to continue their efforts until President Hosni Mubarak steps down, al-Masry al-Youm reported.
"They want us to be a humiliated people, a quiescent people, and an oppressed people ... But no, and 1,000 nos," he said.
He said Egyptians of all backgrounds support the demonstrations, which are now in their 11th day.
"Egypt taught the world dignity and democracy," the imam said.
"Do not leave the square until your demands are met ... (continue) until victory."
His prayers Friday were heard by tens of thousands of people. After the prayers, protesters sang the national anthem and voiced anti-government demands as demonstrations spread throughout the country.