Mubarak said in a nationally televised address Thursday that protesters' demands are "just and legitimate," but said he was "determined to fulfill what I have promised."
Mubarak said he will remain in office until September and that he is transferring some powers to Vice President Omar Suleiman.
Shortly after Mubarak's speech, Suleiman also spoke to the nation, telling protesters to go home and help rebuild the country.
The development caps 17 days of anti-government protests that has drawn tens of thousands of people demanding the 82-year-old to resign immediately.
Egypt's military officials had earlier told protesters that their demands would be met, leading the masses to believe he would step down.
President Barack Obama was closely monitoring the situation while traveling to Michigan.
Obama assured Egyptians the U.S. will help its Middle Eastern ally shift from chaos to democracy, provided the government change is genuine.
However, Mubarak defiantly told the world that he would not let foreign powers intervene.
Before his speech was even over, protesters angrily chanted, "Leave, leave, leave."
Mubarak said he was pained about the deaths that have occurred since protests began, adding that the blood of the victims will not go in vain. The United Nations and Human Rights Watch estimate that 300 people have been killed in Egypt's protests.
A few weeks ago, Mubarak agreed to not seek re-election, but that made demonstrators angrier.
"It means it's going to continue for quite a while," said James Gelvin, a UCLA history professor. "We don't know what's going to happen, but the protesters are not backing down and Mubarak is not backing down."
America's 30-year alliance with Mubarak has many Egyptians looking at the U.S. with anger.
"Where is America now?" said one protester. "America should stand with us, should support us, not support the government."
All eyes are now on the Egyptian military, which seems to be supporting Mubarak for the time being.
ABC News and the Associated Press contributed to this report.