CAIRO  The government of Egypt’s authoritarian president, Hosni Mubarak, shook Monday night, as the Egyptian Army declared that it would not use force against protesters demanding his ouster and, in an apparent response, Mr. Mubarak’s most trusted adviser offered to talk with the opposition.

Those statements, along with the damage to Egypt’s economy, appeared to weaken Mr. Mubarak’s grip on power just two weeks after a group of young political organizers called on Facebook for a day of protest inspired by the ouster of another Arab strongman, in Tunisia.

Hundreds of thousands have turned out into the streets over the last six days, and organizers called on millions of Egyptians to protest on Tuesday.

Within hours on Monday, the political landscape of the country shifted as decisively as it had at any moment in Mr. Mubarak’s three decades in power. The military seemed to aggressively assert itself as an arbiter between two irreconcilable forces: a popular uprising demanding Mr. Mubarak’s fall and his tenacious refusal to relinquish power.