CAIRO — The death toll surpassed 500 on Thursday from Egypt’s bloodiest crackdown on supporters of its deposed Islamist president, as violent new protests erupted in the country and world condemnation widened, including an angry response by President Obama and calls for a suspension of European economic aid.In defiance of calls for restraint, Egypt’s Interior Ministry warned protesters that police officers were authorized to use lethal force to protect themselves. The ministry also promised to punish any “terrorist actions and sabotage” after at least two government buildings were burned early Thursday.“The ministry has given instructions to all forces to use live ammunition in the face of any attacks on establishments or forces within the framework of the regulations of using the legitimate right of self-defense,” the ministry said in a statement. “All the forces assigned to securing and protecting these establishments were provided with the weapons and the ammunition necessary to deter any attack that may target them.”The scorched-earth assault by security forces on Wednesday, which razed two protest camps in Cairo set up by backers of the deposed president, Mohamed Morsi, was far more ferocious and extensive than the gradual pressure promised by the interim government that replaced him.It was the easily the most violent of the three deadly suppressions that have roiled Egypt since Mr. Morsi, Egypt’s first freely elected president, was forcibly removed from power by the armed forces six weeks ago, plunging the country into its worst crisis since the ouster of Mr. Morsi’s authoritarian predecessor, Hosni Mubarak, in the 2011 revolution.Despite the growing tally of dead, Muslim Brotherhood supporters of Mr. Morsi exhorted followers to take to the streets on Thursday, defying the newly imposed state of emergency and reflecting a backlash against the military-appointed successors to Mr. Morsi’s administration, who appear determined to crush the Islamists as a political force.Hundreds of Mr. Morsi’s supporters marched through Alexandria, Egypt’s second-largest city, clashing with the police. In Giza, across the Nile from Cairo near the pyramids, Islamists attacked provincial headquarters with Molotov cocktails and set it on fire. Islamists also blocked the main highway encircling Cairo.In his first response to the Wednesday mass killings, Mr. Obama strongly condemned the Egyptian government’s use of brute force to crush the protests and said the United States had canceled military exercises with the Egypt’s armed forces scheduled for next month. Mr. Obama also warned of further unspecified steps if Egypt’s interim leaders continued down what he called a “more dangerous path.”But he said nothing about cutting the $1.3 billion in annual military aid that the United States provides to Egypt and acknowledged that the United States had historically regarded the country as a friend and a “cornerstone for peace in the Middle East.”