CAIRO — Egypt’s powerful military backed President Hosni Mubarak’s plan to stay in office until September elections, enraging hundreds of thousands of protesters who deluged squares in at least three major cities today, marched on presidential palaces and broke through army barricades at the state TV building — key symbols of the authoritarian regime.

The army’s show of solidarity with the president was a heavy blow to protesters who called on the military to take action to push Mubarak out after he announced Thursday night that he would hand most of his powers to Vice President Omar Suleiman but remain in office.

The Armed Forces Supreme Council, the military’s highest body, depicted itself as the champion of reform in its latest statement.

Trying to win the trust of an angry and skeptical population, the army promised to make sure Mubarak lifts hated emergency laws once protests end. Mubarak and Suleiman had only given a vague timetable for ending the law.

Still, the profound disappointment that Mubarak did not step down on Thursday turned to rage today as protests escalated.

“What are you waiting for?” one protester yelled in the face of an army officer outside Mubarak’s main palace, Oruba, in northern Cairo, where a crowd of demonstrators grew to more than 2,500. “Did you pledge your allegiance to the president or the people?” another shouted.