The generals' strong words signaled the governing military council will tighten its grip on power, further infuriating activists who have demanded an end to army rule and a transition to democracy.
Egypt's Coptic church harshly criticized the government for its actions in crushing the protests and accused it of allowing repeated attacks on Christians to go unpunished.
The clashes Sunday night were the worst sectarian violence since the uprising that ousted Hosni Mubarak eight months ago. The riots laid bare the volatility of Egyptian society a month before the start of parliamentary elections that will help define the country's future political landscape.
In a statement, the Coptic Church, which represents about 10 percent of Egypt's 85 million people, accused security forces of failing to stop anti-Christian agitators from turning what started out as a peaceful protest against church attacks into a sectarian riot in which at least 26 people, mostly Christians, were killed.
"Strangers got in the middle of our sons and committed mistakes to be blamed on our sons," the church said in a statement issued after its spiritual leader, Pope Shenouda III, met with 70 bishops.
"The Copts feel that problems are repeated and the perpetrators go unpunished."
The statement reflected the growing fears of Egypt's Copts, the largest Christian community in the Middle East, at a time when a security vacuum has left them vulnerable to a growing Islamist movement in the post-Mubarak era.
The military, which activists blamed for not doing enough to protect the Christian protesters, issued a stern warning that it intended to crack down hard on future protests.
In a statement, the military council said it will take the "necessary precautions to stabilize security" and use the full weight of the law to prosecute individuals involved in violence, whether by participation or incitement.
In an apparent response to concerns it will use the violence as an excuse to prolong its rule, the council pledged to make good on its promise to hand over power.
Many activists say the generals are likely to take advantage of the nation's tenuous security to stay in power long enough to find a candidate they approve of to run for the presidency.
A timetable floated by the military has slated presidential elections for late next year. If that holds true, then the military will have been in power for almost two years before it steps down.
"We all know that the military council is trying to sow religious strife to stay in power and extend emergency law," said Maha Adel Qasim, a 28-year-old Muslim wearing a head scarf who joined Christians demonstrating outside a hospital where victims' bodies were taken.
"We want international protection," screamed Walid Romani, a Christian, as others outside the hospital chanted for Egypt's military ruler, Field Marshal Hussein Tantawi, to step down.
"The army incites sedition to remain in power," declared Mariam Ayoub, a relative of a slain Christian protester, Michael Mosaad. "They tell all of us that this is what happens without emergency laws."
Sunday's clashes, which raged over a large section of downtown Cairo, began when about 1,000 Christians tried to stage a peaceful sit-in outside the state television building. The protesters said they were attacked by "thugs" with sticks and the violence spiraled out of control after a speeding military vehicle jumped onto a sidewalk and crushed some Christians.
The attack on Christians swelled after state television called on viewers to rush to the army's rescue, casting the Christians as a mob seeking to undermine unity between the people and the military.
The crowd grew to 10,000, and many Christians were set upon by bands of young Muslim men armed with sticks, swords, firebombs and firearms. The assailants later roamed the streets looking for Christians to beat up. In some cases, they pulled men and women suspected of being Christian out of taxis and private cars.
Police and army troops did not intervene.
Three soldiers and an off-duty policeman were among the 26 people killed; some 500 people were wounded.
Egyptian Prime Minister Essam Sharaf blamed foreign meddling for the troubles, claiming it was part of a "dirty conspiracy."
"Instead of moving forward to build a modern state on democratic principles, we are back to seeking stability and searching for hidden hands -- domestic and foreign -- that meddle with the country's security and safety," Sharaf said.
In Washington, the White House said President Barack Obama was deeply concerned about the violence in Egypt and cautioned that it should not stand in the way of "timely elections and a continued transition to democracy."
The European Union called on Egypt's military rulers to guarantee freedom of worship and emphasized the importance of religious plurality and tolerance.
The role played by roaming gangs of "thugs" in violence since Mubarak's ouster has been the subject of intense speculation, with conflicting explanations of their motives and origins. They were initially thought to be Mubarak loyalists, but in some cases have been residents angry over months of near constant protests.
Amr Moussa, a former foreign minister and a presidential hopeful, blamed the clashes on hard-liners seeking to destabilize the revolution, not religious intolerance.
They "want to stab the revolution and the political process. The situation is critical and there are dangers of civil war," he warned.