Story highlights At least 51 people were killed, state media reports

The Muslim Brotherhood's party says peaceful protesters were slain

Egypt's Interior Ministry says hundreds of rioters were arrested

Demonstrators jump into the Nile to escape arrest

Clashes erupted between demonstrators and security forces in Egypt on Sunday, leaving 51 people dead and more than 260 injured, state media reported.

The violence started early Sunday afternoon as Muslim Brotherhood protesters marched in different neighborhoods in Cairo and across the country.

In Egypt's capital, people swam across the Nile River to escape arrest as military armored personnel carriers supported police clearing the streets of protesters.

Tear gas filled the air and security forces with batons beat some of the protesters they detained.

It was another powerful sign that Egypt's military-backed interim government will go to almost any measure to shut down the Muslim Brotherhood's protests.

But in nearby Tahrir Square, the scene was drastically different; throngs of people celebrated Egypt Armed Forces Day at a festive event that included dancing and fireworks.

As thousands of Muslim Brotherhood protesters marched along the Nile from Old Cairo toward Tahrir, security forces blocked their path and quickly dispersed the crowd.

Health Ministry official Khaled El-Khatib told CNN that the death toll included 19 people killed in Cairo, 20 people killed in Giza, four people killed in Beni Suef and one person killed in Minya. Nationwide, 268 people were injured, state media reported.

In a statement, the Muslim Brotherhood's Freedom and Justice Party decried what it called "crimes of violence and murder committed today against peaceful protesters," adding that it holds the leaders of the coup that ousted former President Mohamed Morsy responsible. Egypt's Interior Ministry said it had arrested 423 "rioters" on Sunday.

In September, an Egyptian court banned all activities of the Muslim Brotherhood and froze its finances, drawing complaints from the international community. At the United Nations General Assembly, Egypt's interim foreign minister sought to quell these concerns.

Nabil Fahmy said Egypt will hold elections in the spring. He also argued that the political process is open to all "as long as they are committed to the renunciation of violence and terrorism and acts of incitement to them."

On Sunday, protesters from the Muslim Brotherhood said they would accept nothing less than the reinstatement of the government led by Morsy. But supporters of the military in Tahrir Square remained adamant that that shouldn't happen.

Neither side appeared willing to compromise.