Speaking on state TV, Mr Mubarak promised constitutional reform, but said he wanted to stay until the end of his current presidential term.
The announcement came as hundreds of thousands rallied in central Cairo urging him to step down immediately.
The demonstration was the biggest since protests began last week.
The BBC's Yolande Knell in Tahrir Square in central Cairo says it remains to be seen whether Mr Mubarak's statement is enough for protesters, and adds that it could divide Egyptians.
She says there are some determined to carry on, while others think these are major concessions and that the protests have gone far enough.
Mr Mubarak said he would devote his remaining time in power to ensuring a peaceful transition of power to his successor.
"My first priority is to restore peace and stability in our country, to ensure the peaceful transition of leadership, and to ensure that the responsibility goes to whomever the people of Egypt choose in the next election. I do not intend to stand for election again," he said.
