There are generally two stories about how reliable the police force is in the southern Egyptian city of Assiut, and one of those is told by the police.

“We are present. We are efficient, and we work around the clock,” said Alaa Abdelsalam, one of the city’s two district police chiefs, in his office in an elegant, colonial-era station on a recent night, a fish tank bubbling to his right. An entourage of officers nodded in agreement.

Just about everyone else in the city disagrees.

“If you call the police, the police are not going to come,” said Alam al-Din Ibrahim, the manager of a car-parts shop in Assiut, where residents say crime is on the rise. “You can call on God to help you,” he said.

It’s a sentiment that is becoming widespread in Egypt, where one violent protest after another has threatened to upend the Arab world’s largest country and send an already devalued currency and government bureaucracy into rapid free fall.

And in Assiut, the sprawling capital of Egypt’s poor and conservative south, Gamaa Islamiya — the Islamist extremist group that carried out a 1997 massacre of 62 people in the historic city of Luxor — has offered to lend a hand.

Assiut has long been a stronghold for Gamaa Islamiya, whose name means “the Islamic group.” It was here and in other cities along Egypt’s rural Nile Valley where Islamist radicals waged a violent insurgency against the governments of Anwar Sadat and Hosni Mubarak in the 1980s and ’90s. Many group members and affiliates consequently spent more than a decade in jail.

Group leaders in the Nile Valley and in Cairo now say that their violent days are over but that they still want to see Islamic law implemented in Egypt. After the country’s 2011 revolution created space for Islamist radicals to flex their muscles, the group developed a political party, and local leaders have formed what they call “popular committees’’ to help fill a void two years after Mubarak’s fall.

“Things had gotten out of hand,” said Shaaban Ali, a group leader in Assiut.

Several weeks ago, Gamaa Islamiya volunteers — in neon vests with the group’s name and “order committee” printed on the back — began distributing butane gas cylinders to the poor, along with subsidized meat. When Assiut’s trash collectors went on strike, the group put up fliers to recruit workers for a new trash-collection service it would run. They seized “thugs” accused of theft and handed them over to the police. They even rescued kidnapping victims from their captors, Ali said.

And when the national police force receded amid a nationwide strike, the Islamist volunteers offered to take over its work, too.

But Gamaa Islamiya’s initiative didn’t go over as well as members of the group had planned.

Christians, who make up a sizable minority in Assiut (as in Egypt overall), and liberal political leaders reacted with alarm, fearing a more forceful push for Islamic law. “The problems are coming from them. And that’s not just me personally saying that — it’s everyone,” said Rafaat Hakim, a Christian teacher in a nearby village.

Other residents feared that it was a dangerous power grab or, at the very least, a quest for votes in the upcoming parliamentary election. Even the Assiut police force perked up a little — and suddenly, awkwardly, went back to work.

The worry among police, said Mahmoud Abdel Meguid, a sergeant, was that the Islamist group “could exploit this situation.” He added: “We’ve heard that they have always had militias, which they could use and dispatch.”

Gamaa Islamiya’s local leader, Tarek Bedeir, says that the group has no weapons and that its move merely “embarrassed” the police force. But the talk of vigilantism among Islamists has made Assiut an early test of whether the embattled government of President Mohamed Morsi can resurrect the authority of a police force widely associated with old regime abuses.

Under fire from protesters and other angry citizens, the national Egyptian police force is steadily losing ground in many places around the country. Police strikes added to the troubles this month as thousands of officers and low-ranking riot cops walked off the job in protest of a government that they, too, said had failed them. Egypt’s attorney general has even invited citizens to start doing some of the policing themselves.

Over the weekend, residents of Mahallit Zayad, a village in the Nile Delta, beat and dragged two suspected thieves through the streets before stringing them up by their feet at a bus stop. Both men died.

Other tales of vigilante justice from urban centers to rural villages have crept, with increasing frequency, into the nation’s newspapers and conversations in recent months. Egypt’s justice minister, Ahmed Mekki, warned Monday that public lynchings could mark “the death of the state.”

For some in Assiut, it hasn’t been such a bad thing that Gamaa Islamiya has offered to get things under control.

“They are very good at delivering gas and bread,” said Mohamed Ali, the owner of a gold shop in the city center.

Others said desperate times mean that Assiut’s residents can’t afford to be picky. “I just want anyone to give me security. Who, it doesn’t matter,” said Ibrahim, the car-parts shop manager.

Outside the Abu Bakr al-Sadiq Mosque, where Gamaa Islamiya keeps its local headquarters, a pair of bearded men directed traffic in the blinding sunshine of a recent afternoon. The police strike had ended, but Gamaa Islamiya was still “helping.”

Nearby, Bedeir, the group’s leader, fielded a phone call from a distraught woman who said her brother had overdosed on drugs. He promised to send some popular committee members to haul the man away.

“Even if the police were present, people prefer resolving conflicts peacefully with us than going to the cops,” said Shaaban Ali, another group leader. “The cops will make them go round in circles.”

Over at one of Assiut’s police stations along the Nile, the tension ignited by such criticism was palpable. “For Gamaa Islamiya to replace the police, the sun would have to rise in place of the moon,” scoffed Mohamed al-Amir, a deputy head of investigations.

But Ali insists that they’ve got it all wrong. The old regime made a scapegoat of Gamaa Islamiya, he said, and now the group is finally getting some redemption. “People listen to us because they love us,” he said.

“No matter how able we become, we are only assisting,” Ali said. “We cannot replace the government.”

Sharaf al-Hourani in Assiut contributed to this report.