CAIRO — Egypt’s army-appointed government handed in its resignation Monday, an apparent gesture to thousands of protesters in Cairo’s Tahrir Square who clashed for the third straight day with security forces in violence that has killed at least 24 people and posed the most sustained challenge yet to the rule of the military.

The crowds in Tahrir, which had grown to well over 10,000 after nightfall, broke out into cheers with the news of the cabinet’s move, chanting “God is great.” But there was no sign the concession — resignation of a virtually powerless cabinet — would break their determination to protest until the military steps down completely and hands over power to a civilian government.

Beating drums, the protesters quickly resumed their chants of “the people want the ouster of the field marshal,” a reference to Field Marshal Hussein Tantawi, the head of the council of generals that has ruled the country since the Feb. 11 fall of authoritarian president Hosni Mubarak.

The Supreme Council of the Armed Forces, which Tantawi heads, did not immediately announce whether it would accept the mass resignation. Many Egyptians had seen the government, headed by Prime Minister Essam Sharaf, as a mere facade for the military and either unable or unwilling to press ahead with democratic reform or take action to stem increasing turmoil and economic crisis around the country.

The anger, however, has ultimately been focused on the generals themselves, who many activists accuse of acting as abusively as Mubarak’s regime and of intending to maintain their grip on power.

The turmoil comes only a week before Egypt is to start key parliamentary elections, which many had hoped would be a landmark in the transition to a democracy. Instead, they have been overshadowed by the standoff over the military. Activists believe that no matter who wins the vote, the generals will dominate the next government as much as they did Sharaf’s. The military says it will hand over power only after presidential elections, which it has vaguely said will be held in late 2012 or early 2013.

If Monday’s resignations are carried out, a crucial question will be who will replace the cabinet. Some in the square demand the military immediately hand over all its authority to a national unity government made up of multiple factions.

“We are not clearing the square until there is a national salvation government that is representative and has full responsibility,” said activist Rami Shaat.

Violence has steadily escalated the clashes began Saturday, when police tried to clear several hundred protesters in the square. Repeated attempts to clear the protesters from Tahrir have failed, and a death toll that quadrupled overnight from Sunday has only brought out more and angrier protesters. The protests have spread to other cities around the country, including the coastal city of Alexandria, where one of the deaths took place.

Throughout the day on Monday, black-garbed security forces fired tear gas, rubber bullets and — many protesters said — live ammunition at young men in the streets around Tahrir. The protesters hurled stones and threw back the gas canisters that clattered across the pavement, streaming stinging clouds.

Sounds of gunfire crackled around the square, and a constant stream of injured protesters — bloodied from rubber bullets or overcome by gas — were brought into makeshift clinics set out on sidewalks, where volunteer doctors scrambled from patient to patient.

“I will keep coming back until they kill me,” said Mohammed Sayyed, his head bandaged from a rubber bullet wound. “The people are frustrated. Nothing changed for the better.”

“What does it mean, transfer power in 2013? It means simply that he wants to hold on to his seat,” said Sayyed, holding two rocks in his hand, ready to throw, as he took cover from tear gas in a side street off Tahrir.

During an overnight assault, police hit one of the field clinics with heavy barrages of tear gas, forcing the staff to flee, struggling to carry out the wounded. Some were moved to a nearby sidewalk outside a Hardees fast food restaurant. A video posted on social networking sites showed a soldier dragging the motionless body of a protester along the street and leaving him in a garbage-strewn section of Tahrir.

An Egyptian morgue official said the toll had climbed to 24 dead since the violence began Saturday — a jump from the toll of five dead around nightfall Sunday, reflecting the ferocity of fighting through the night. Hundreds have been injured, according to doctors in the square.

Amnesty International condemned the violence.

“While the Egyptian authorities have a duty to maintain law and order, they must not use excessive force to crack down on peaceful protests, something that poses a severe threat to Egyptians’ rights to assembly and freedom of expression,” the London-based group said in a statement.

The military on Sunday night issued a statement saying it did not intend to “extend the transitional period” and vowed not to let anyone hinder the “democratic transition.” The government has said elections will be held on schedule, starting on Nov. 28 and extending over numerous phases for several months.

Election politics have complicated the protesters’ bid to launch what some of them tout as a “second revolution.”

The loose coalition of groups that led the 18-day uprising that ousted Mubarak in February is fragmented. In particular, the Muslim Brotherhood, which gave the first revolution powerful muscle, so far refuses to take to the streets again, fearing the turmoil will derail the parliament elections, which it expects to dominate. Some of the secular protesters in Tahrir are worried the vote will give too much power to the fundamentalist group.

Monday afternoon, protesters angry at the Brotherhood for not participating jeered and threw water bottles at a prominent figure in the group, Mohammed el-Beltagy, as he visited the square.

Earlier in the day, the military council made another apparent attempt at a concession, issuing a long-awaited anti-graft law that bans anyone convicted of corruption from running for office or holding a government post.

But the law falls far short of demands by many that all members of Mubarak’s former ruling party be banned from politics.

The protesters’ suspicions about the military were fed by a proposal issued by the military-appointed cabinet last week that would shield the armed forces from any civilian oversight and give the generals veto power over legislation dealing with military affairs. It would also give them considerable power over the body that is to be created after the election to draft a new constitution. Activists already accuse the military of ruling with the same autocratic style of Mubarak.

One of the most prominent democracy proponents in the country, Nobel Peace laureate Mohamed ElBaradei, called on the civilian government to resign and for a national unity government to be formed, “grouping all the factions so it can begin to solve the problems of Egyptians.”

“Power is now in the hands of the military council, which is not qualified to run the country, and the government, which has no authority,” he said on a TV political talk show late Sunday. For the next six months, “we want to see the powers of the military council given completely to a civilian, national unity government, and the military goes back to just defending the borders.”