CAIRO—Egypt's Muslim Brotherhood accused the country's military of massacring dozens of its supporters during dawntime prayers in Cairo on Monday, as Egypt's deadliest clashes in years between the army and Islamists pushed the country toward armed conflict.

At least 53 people were killed and more than 400 wounded, Egypt's official media said, in a clash between the military and supporters of Mohammed Morsi, who had gathered near the site where Mr. Morsi has been held under house arrest since he was ousted as president last week.

Egypt's military denied the allegations of a massacre, saying that soldiers defended themselves after they were attacked with guns and Molotov cocktails, and that 42 protesters, plus a soldier, had been killed.

Monday's violence demonstrated the peril of the military's decision to remove Mr. Morsi, the first freely elected president in the history of the Arab world's largest nation. Despite its relative stability, Egypt is flirting with what several analysts have until now seen as a worst-case scenario—the kind of armed conflicts that have roiled other countries in the so-called Arab Spring of uprisings.

Only last Wednesday, the military said it was responding to popular will by ousting the country's Brotherhood-backed president. Millions of Egyptians cheered. Standing alongside Egypt's military chief, leaders representing the country's Muslims, Coptic Christians and secular opposition promised to form an inclusive interim government.