CAIRO — The Muslim Brotherhood demanded Thursday that Egypt’s military rulers cede control of the government, stepping closer to a long-anticipated confrontation between the ruling generals and the Islamist-dominated Parliament.

In a statement on its Web site and a television interview with one of its senior leaders, the Brotherhood called for the military to allow the replacement of the current prime minister and cabinet with a new coalition government formed by Parliament, which would amount to an immediate handover of power.

The Brotherhood, the formerly outlawed Islamist group, now dominates Parliament. It had previously said it was content to wait until June, when the generals had said they would hand over the power they seized at the ouster of President Hosni Mubarak last year. And signs were accumulating of a general accord between the military and the Brotherhood over the terms of a new constitution expected to be ratified before the handover. The Brotherhood’s shift comes on the eve of the Feb. 11 anniversary of Mr. Mubarak’s downfall, when other activists around the country have called for a general strike to demand the end of military rule — a call the Brotherhood has previously resisted.

But the group is also changing its position at a time when the military-controlled government appears overwhelmed by domestic and foreign crises, including a deadly soccer riot last week followed by five days of violent protests, a standoff with Washington that has imperiled billions of dollars in United States aid and international loans, and an economy teetering on collapse.