CAIRO — Egypt’s interim military rulers faced the most significant challenge in a week of escalating protests on Friday as the Obama administration threw its weight behind the Egyptians who flooded into Tahrir Square to demand that the generals relinquish power, and new signs of unity emerged among street protesters and the political elite.

The developments added to a convergence of pressures on the tenuous legitimacy of the military-led government in Egypt. It was once held in high regard for helping to usher out President Hosni Mubarak 10 months ago, but it is now increasingly criticized for exerting the same oppressive force as he once did.

“The military has got to be frightened to death,” said Robert Springborg, a scholar of the Egyptian military at the Naval Postgraduate School in Monterey, Calif. The crux of the protesters’ demands, he said, has now gone beyond the ouster of a president to threaten the underlying power structure in place since Gamal Abdel Nasser’s 1952 military coup. “It would be the first time since 1952 that a civilian was in the driver’s seat,” Mr. Springborg said.

The White House statement, issued shortly after 3 a.m. in Washington on Friday to coincide with the Egyptian morning, took aim at the ruling military council’s appointment late Thursday of a new prime minister charged with appointing a government to execute the generals’ directions, without independent authority. “The United States strongly believes that the new Egyptian government must be empowered with real authority immediately,” the White House said in the statement.