CAIRO — Millions of Egyptians streamed into the streets of cities across the country on Sunday to demand the ouster of their first elected head of state, President Mohamed Morsi, in an outpouring of anger at the political dominance of his Islamist backers in the Muslim Brotherhood.

The scale of the demonstrations, coming just one year after crowds in Tahrir Square cheered Mr. Morsi’s inauguration, appeared to exceed even the massive street protests in the heady final days of the uprising that overthrew President Hosni Mubarak in 2011. At a moment when Mr. Morsi is still struggling to control the bureaucracy and just beginning to build public support for painful economic reforms, the protests have raised new hurdles to his ability to lead the country as well as new questions about Egypt’s path to stability.

Clashes between Mr. Morsi’s opponents and supporters broke out in several cities around the country, killing at least seven people — one in the southern town of Beni Suef, four in the southern town of Assiut and two in Cairo — and injuring hundreds. Protesters ransacked Brotherhood offices around the country. In Cairo, a mob of hundreds set fire to the almost-empty Brotherhood headquarters, pelting it with stones, Molotov cocktails and fireworks for hours. A few members hiding inside the darkened building fired bursts of birdshot at the attackers, wounding several, but the police and security forces did nothing to stop the assault or the arson.

Demonstrators said they were angry about the near total absence of public security, the desperate state of the Egyptian economy and an increase in sectarian tensions. But the common denominator across the country was the conviction that Mr. Morsi had failed to transcend his roots in the Brotherhood, an insular Islamist group officially outlawed under Mr. Mubarak that is now considered Egypt’s most formidable political force. The scale of the protests across the country delivered a sharp rebuke to the group’s claim that its victories in Egypt’s newly open parliamentary and presidential elections gave it a mandate to speak for most Egyptians.