Kamal el-Ganzouri said that military ruler Field Marshal Hussein Tantawi has no intention of staying in power and he would not have accepted the job if that was the case.
But the move was quickly rejected by the tens of thousands of protesters packed into Cairo's Tahrir Square.
In a televised news conference, the 78-year-old prime minister looked uncomfortable, grasping for words and repeatedly pausing.
He says he won't be able to form a government before parliamentary elections start on Monday. The election is to be staggered over multiple stages that end in March, and the military said Friday it would extend the voting period to two days for each round in an apparent effort to boost turnout due to the current unrest.
El-Ganzouri is from the era of the ousted leader Hosni Mubarak, and activists accused the generals of trying to extend the old guard.
In the meantime, a group of local Egyptians plan to hold a protest outside the U.S. federal building in Westwood on Friday to show support for the Egyptian uprising.
The Associated Press contributed to this story.