CAIRO—Early Friday, 16 months after ousting former President Hosni Mubarak from power, Egypt's young revolutionaries huddled with leaders of the Muslim Brotherhood, once close allies, and pleaded for help to save the revolution.

A pair of Supreme Court rulings a day earlier had dissolved the Parliament—which had been filled this year through free elections—and returned legislative powers to the Egyptian military. The rulings came a day after the declaration of martial law, which those at the meeting agree had amounted to...