Citizens have grown bolder in taking matters into their own hands following the 2011 uprising. The country's once powerful and feared police force was left weakened after the revolt.
Thousands of policemen are now on strike to demand better working conditions and they also refuse to confront widespread protests against President Morsi's leadership.
Some of the striking police officers allege that Morsi's Muslim Brotherhood is attempting to control them. The Brotherhood denies that.
Al-Muneer, the Brotherhood spokesman in Gharbiya, accused some policemen of hoping for a collapse of security to pave the way for the old regime to return to power. That same accusation has been leveled at the police repeatedly, both in the midst of the uprising and the aftermath.
He said the Brotherhood fully rejects the killings and said citizens should have arrested the two but then handed them over to police.
The attorney general's call for citizen arrests a week ago was prompted by the police strike and deteriorating security. Opponents of his call fear that this is a prelude to the substitution of police by militias, including those belonging to other Islamist groups allied with Morsi and the Islamic fundamentalist Brotherhood.
Interior Minister Mohammed Ibrahim, who oversees the country's police, met with officers and low-ranking policemen to hear their demands on Sunday.
Two days earlier, Morsi attended traditional Islamic prayers at a Cairo-based camp for riot police. He praised the force despite public criticism over their violent response to anti-government demonstrations.
Morsi is facing an onslaught of challenges, from the police strikes to an increasing number of violent sexual attacks on women to mounting diesel shortages that have crippled daily life for millions in Egypt.
And although vigilante killings are not frequent in Egypt, there have been similar attacks in the past two years.
In 2012 in northern Sharqiya province, police said relatives of a man who was killed when muggers tried to steal his car lynched one of the thieves. They then burned his body while it hung from a light pole.
Another case that year was in the Nile Delta province of Mansoura, where relatives of a victim took justice into their own hands and lynched two suspected killers.
Anger at Morsi was on display again Sunday, when protesters took their demands to the Brotherhood's doorstep. Hundreds clashed with police who fired tear gas at the crowd outside of the Islamist group's Cairo headquarters.
The crowd was responding to an assault on journalists, who claimed they were attacked by Brotherhood members Saturday evening during coverage of a meeting.
The journalists said that after a group of activists sprayed anti-Brotherhood graffiti on the ground outside the group's Cairo headquarters, the Brotherhood guards attacked with sticks and chains.
Brotherhood spokesman Mahmoud Ghozlan said in a statement that guards outside the building were provoked and insulted by the activists and journalists.
Many of the group's offices were attacked across the country in December during violent protests over the drafting of the constitution.
Dozens of journalists rallied outside their syndicate in the capital Cairo against the incident.
Diaa Rashwan, the newly elected head of the syndicate who replaced a figure considered by most journalists as pro-Brotherhood, said he would file a lawsuit against the Brotherhood spokesman for suggesting that journalists had incited the violence.
The opposition party Al-Dustor, led by Nobel laureate Mohamed ElBaradei, blamed the Brotherhood's leadership for allegedly encouraging "militias" loyal to the group to join the fight.
There were clashes on Saturday during protests against Morsi and the Brotherhood during the president's trip to the impoverished governorate of Sohag. The presidency on Sunday denied that opposition protesters had tried to storm the hall where Morsi had been speaking, despite video that showed the attempt.