In his televised address, el-Beblawi said the government could not indefinitely tolerate a challenge to authority that the 6-week-old protests represented.
"We want to see a civilian state in Egypt, not a military state and not a religious state," he said.
But the resignation of ElBaradei, the former head of the U.N. nuclear agency and a figure widely respected by Western governments, was the first crack to emerge in the government as a result of the violence.
ElBaradei had made it clear in recent weeks that he was against the use of force to end the protests. At least 250 people have died in previous clashes since the coup that ousted Morsi, Egypt's first freely elected president.
On Wednesday, his letter of resignation to interim President Adly Mansour carried an ominous message to a nation already torn by more than two years of turmoil.
"It has become difficult for me to continue to take responsibility for decisions I disapprove of, and I fear their consequences," he said in the letter that was emailed to The Associated Press. "I cannot take responsibility before God, my conscience and country for a single drop of blood, especially because I know it was possible to spare it.
The National Salvation front, the main opposition grouping that he headed during Morsi's year in office, said it regretted his departure and complained that it was not consulted beforehand. Tamarod, the youth group behind the mass anti-Morsi protests that preceded the coup, said ElBaradei was dodging his responsibility at a time when his services were needed.
Sheik Ahmed el-Tayeb, the powerful head of Al-Azhar mosque, Sunni Islam's main seat of learning, also sought to distance himself from the violence. He said in a statement he had no prior knowledge of the action.