Morsi and the Brotherhood have made it clear that they do not want the military to play any political role.

But that did not stop el-Sissi from extending an invitation to the opposition and Islamist leaders loyal to Morsi to sit down informally over lunch to defuse a crisis over presidential decrees issued in November that gave Morsi near absolute powers. The decrees have since been rescinded.

Under pressure from the Brotherhood, el-Sissi withdrew the invitation just hours before the meeting was to start.

Morsi appointed el-Sissi less than two months after taking office as Egypt’s first freely elected president. The Aug. 12 appointment followed Morsi’s bold decision to retire the nation’s two top generals, restoring the full powers of the president’s office and ending a months-long power struggle between the two sides. Before Morsi’s move, the military had the power to legislate since the legislature was dissolved in June by a court ruling. The military also held veto power over a panel that was drafting a new constitution at the time.

Still, few ever took el-Sissi to be the president’s man. And there were doubts that six decades of de facto military rule had come to an end or that the military had been relegated to playing second fiddle to civilians.

Morsi and his Islamist supporters passed up a major opportunity to curb the military’s power — something that would have meant a major confrontation with the generals.

The new constitution drafted by Islamists enshrined the military’s near-complete independence and kept its vast economic interests above oversight, against the wishes of many who participated in the 2011 revolt.

With chaos in the country deepening, chants calling for military intervention during street protests, last heard en masse during the uprising, are making a timid comeback.

‘‘Millions of Egyptians want the army to come back and deliver us from chaos,’’ Ibrahim Issa, host of a political talk show on television, said this week.

‘‘This is the sentiment on the Egyptian street, and ignoring it is stupid,’’ said the popular Issa, a harsh critic of Morsi, the Brotherhood and the military when it was in power.

Since taking office in June 2012, Morsi has made little progress in tackling Egypt’s pressing problems — steep price increases, surging crime, deteriorating services and fuel shortages.

The Brotherhood, which dominates parliament and the government after winning every election since Mubarak’s ouster, is accused of monopolizing power. And Morsi has been criticized for failing to deliver on a promise of an inclusive government representing the Christian minority, liberal and secular political factions, and women.

The highly charged political climate and the collapsing economy could make a military takeover seem like a welcome development in some corners of Egypt — or at least a necessary evil that could salvage the nation.

But the military may not be willing to insert itself directly again in politics or governance. Its prestige was badly tarnished by scathing criticism of its handling of the post-Mubarak transition period.

A few days into the uprising, Mubarak ordered the army into the streets to replace a police force that melted away when confronted with massive public outrage over decades of abuse.

With the country in chaos and paralyzed, the military later sided with protesters who demanded that Mubarak leave office. A council of ruling generals took over the reins of power, but the relationship soon turned sour.

Activists and pro-democracy groups accused the generals of widespread human rights violations during their rule, including the torture of detainees and the trial of at least 10,000 civilians before military tribunals.

The military later made good on its promise to hand over power to an elected government, although Morsi and his Brotherhood would clearly not have been the generals’ choice if they had to make one.

With that history in mind, there are serious questions about whether a military intervention can even solve any of Egypt’s problems in a time short enough to satisfy a population seething with anger over the chaos and hardships of the last two years.

The military would be risking more vilification if it does not move the country onto firmer ground quickly.