CAIRO—Thousands of protesters clashed with Egyptian security forces for a third straight day Monday in an increasingly violent showdown with the country’s ruling generals, who face unprecedented and rapidly escalating discontent less than a week before scheduled elections.

As night descended on Cairo, scores of unconscious protesters continued to be dragged from smoke and teargas-clogged side streets leading into Tahrir Square, the heart of Egyptians’ protests early this year. Fighting between security forces and protesters have left 33 people dead since Saturday morning and injured more than 1,000, say health officials, in the deadliest clashes since the Feb. 11 abdication of President Hosni Mubarak.

Egyptian media also reported growing clashes in Alexandria, Suez and other Egyptian cities, accounts that weren’t immediately possible to verify. Protest leaders called for a million-man demonstration in Tahrir Square on Tuesday.

Thousands of protesters clashed with Egyptian security forces for a third straight day Monday in an increasingly violent showdown with the country’s ruling generals. Matt Bradley on The News Hub has the latest from Cairo.

In a further sign of snowballing pressure on Egypt’s ruling generals, the country’s civilian cabinet submitted its resignation to the military late Monday evening, according to Egypt’s state-run television. It remained unclear whether the military would accept the resignation.

Egypt’s military had been hailed just months ago as the guarantor of the country’s revolution and the guardians of its transition to democracy. But now, protesters who overthrew Mr. Mubarak are setting their sights on what is perhaps an even more daunting objective—challenging the military itself, an institution that has stood at the core of Egyptian power for more than 60 years and was left whole after Mr. Mubarak’s fall.

“The people want the downfall of the field marshal,” thundered the crowd at Tahrir Square, referring to Field Marshal Hussein Tantawi, the head of Egypt’s ruling military council and the former minister of defense under Mr. Mubarak.

Military officials, seen as Egypt’s true arbiters of power, enjoy a privileged status atop Egyptian society, with vast business and real-estate holdings. Ex-generals have ruled Egypt since the toppling of the monarchy in 1952.

But frustration has exploded in recent days among protesters—ranging from pro-democracy activists to Islamic parties—that the military has been slow to pave the way for a transition to democracy and has continued many repressive policies common under Mr. Mubarak.

The latest upwelling has cast doubt over the fate of parliamentary elections due to begin on Nov. 28. On Monday, the country’s most powerful opposition group, the Muslim Brotherhood, said they had suspended all major campaign events due to the violence, though they said they remained committed to holding elections as scheduled.

Other political forces have called for the elections to be postponed and for the military to hand power immediately to a civilian transitional government.

The Supreme Council of the Armed Forces, in a statement on state television late Monday, called on political parties to engage in national dialogue and maintain calm. The SCAF remains committed to holding elections on schedule, according to retired Gen. Sameh Saif al-Yazal, who remains in close contact with the council.

Gen. Yazal also said he expected the military would accept Monday’s cabinet resignations, in contrast with recent instances in which the military has rejected such moves by cabinet ministers. That would pave the way for the formation of a new government, which could help calm protests if it included a broader swath of protest leaders and opposition figures.

Late Monday near Tahrir Square, the wounded, suffering from tear gas or wounds from rubber-coated bullets, were treated in makeshift field hospitals or whisked away by screaming ambulances. The area around Tahrir accounted for the vast majority of the reported deaths, with many fatalities from gas asphyxiation, Egyptian health officials said. They said they expected the number of casualties to rise.

Earlier in the day, about 100 opposition activists were attacked by police as they were on their way to a meeting the head of Cairo security had invited them to in order to discuss ways to calm the situation, opposition leader and Nobel peace laureate Mohamed ElBaradei said via Twitter.

The White House said Monday it is “deeply concerned” about the violence in Egypt and called for restraint.

“The United States continues to believe that these tragic events should not stand in the way of elections and a continued transition to democracy that is timely, peaceful, just and inclusive,” White House press secretary Jay Carney said. “It’s important to step back and remember how far Egypt has traveled this year.”

In what amounted to a shallow concession to protesters, the military on Monday afternoon made good on a weekslong promise to exclude politicians convicted of fraud from serving in public office. The announcement did little to calm protesters, many of whom had sought to bar all officials from the former ruling party from running.

The roots of protesters’ growing frustration with the military were highlighted in a report published Monday by the London-based human rights group Amnesty International, which said the SCAF’s record of human-rights abuses “in some cases exceeds” those under Mr. Mubarak. “Those who have challenged or criticized the military council—like demonstrators, journalists, bloggers, striking workers—have been ruthlessly suppressed,” the report said.

Some 12,000 young activists and demonstrators have been tried before military courts, some in proceedings lasting only a few minutes, and jailed without recourse. Political activists have been tortured and women protesters administered “virginity tests” while in military detention, according to human-rights groups. Many of the country’s leading human-rights groups and activists are facing criminal investigations by military-appointed prosecutors.

The military, meanwhile, has reneged on pledges of a speedy handover of power to civilian rule and tried to dictate a set of constitutional principles that would preserve sweeping powers for the military in any future government.

“After the terrible behavior by the military, our only priority is that we get a civilian government and end the military’s rule, and the brutality and oppression of this military government,” said protester Ahmed Bahgat, a 34-year-old marketing consultant.

Egypt’s Muslim Brotherhood, which until recently had shown a greater willingness to cooperate with the military than many other opposition forces, called security forces’ crackdown on protesters “a heinous crime.” It called for a clear timeline for handover to an elected civilian authority no later than 2012.

But many protesters in the square and other opposition forces appear to have sharpened their demands in recent days, calling for a more immediate transition to a caretaker government. Many protesters said Monday that more promises wouldn’t suffice and that they wouldn’t leave the square until a new civilian government was in charge.

The ability of the Muslim Brotherhood and the country’s liberal forces to agree on a common set of demands could help determine whether the protests succeed in pushing the military from power.

The Brotherhood has said it won’t participate in Tuesday’s demonstrations, underscoring the mutual mistrust and rifts that have hobbled the opposition for months. Still, there appears to be growing agreement between the two camps that the military’s rule must end.

That marks a dramatic reversal of fortunes for the military. Just days ago, the military still appeared on firm ground and seemingly supported by many Egyptians, while the country’s protest movement appeared to be sputtering. The broader Egyptian public had grown largely unenthusiastic about the prospect of a revolutionary double dip.

Many blamed the revolution for persistent economic problems—particularly cratering tourist numbers, dwindling foreign direct investment and a plummeting stock-market index.

The current bout of unrest began Saturday morning, a day after the Muslim Brotherhood and other Islamist groups led a massive rally in Tahrir Square, calling for a quicker transition to civilian rule and protesting the set of constitutional principles drawn up by the military. That rally ended peacefully Friday evening.

But on Saturday morning, security forces cracked down violently on a few dozen protesters who remained on the square overnight.

As in January, when popular anger over heavy-handed police tactics fired the uprising that ousted Mr. Mubarak, Saturday’s move drew angry crowds, swelling with each successive attempt by riot police and soldiers to violently put down the protest on Saturday, Sunday and again on Monday.

By early Tuesday, the square filled to its greatest levels since the three-day uprising began, with 20,000 to 80,000 people there, according to estimates. Many, in a throwback to Tahrir’s days as the revolution’s epicenter earlier this year, erected banners and tents.

—Tamer El-Ghobashy contributed to this article