The main opposition coalition saw the statement on citizen arrests by the attorney general's office as a prelude to the substitution of the police by militias belonging to Morsi's powerful Muslim Brotherhood group and allied Islamist groups who swept to power after Egypt's uprising two years ago.
"It is now clear why the regime insists on pitting the police against the people and relying on security measures to tackle problems that need social, economic and political solutions," the opposition National Salvation Front said in a statement on Monday.
Egypt has been embroiled in wave after wave of political protests since the 2011 uprising that ousted Hosni Mubarak's autocratic regime.
The unrest has been fueled by the entire range of social ills from tenuous security to an unraveling economy and the leadership of Morsi and the Muslim Brotherhood. The Brotherhood controls parliament as well as the presidency and has won every election since Mubarak's ouster.
Morsi's government says the recent wave of protests sweeping many parts of the country is a conspiracy involving both Mubarak loyalists and the mostly liberal and secular opposition to undermine the authority of a democratically elected president.
The president said in a TV interview aired last month that he would like see more regular Egyptians take the initiative in dealing with protesters such as those who block roads. He has repeatedly warned that while peaceful protests are a given in today's Egypt, those who disrupt normal life hurt the economy and scare investors away.
The opposition statement recalled the events of Dec. 5 when Morsi supporters set upon opposition protesters camped outside the presidential palace and later arrested and interrogated dozens of them in makeshift detention centers outside the palace gates.
Later, videos posted on social networks showed the president's supporters hitting and stripping the protesters.
"That, it is clear now, was not unrelated to the plan designed to divide the country as a prelude to the rule of the militias," the opposition front said.
Former lawmaker Mustafa el-Nagar, a liberal opposition supporter, said the statement by the attorney general's office would cause more divisions in the country and empower anyone to make a citizen arrest under false pretenses.
"Under our present circumstances, we cannot open the door for such action because it will open the door to civil war," he said. "This has to be stopped and authorities must back down."
Late Sunday night, the office of the attorney general, the country's top prosecutor, issued a statement encouraging citizen arrests. It was attributed to a senior aide, Hassan Yassin.
Some of the offenses he cited as warranting citizen arrests have been commonplace in Egypt in the two years since the uprising and have become more frequent in recent weeks.
Among them are sabotaging state facilities, blocking roads, disrupting public transport, preventing state employees from reaching their workplace and terrorizing citizens.
The statement coincided with a partial strike by segments of the police to demand better working conditions and, in some cases, to protest what they see as an attempt by the Muslim Brotherhood to control the police. The Brotherhood denies the charge.
Meanwhile, the former jihadist group Gamaa Islamiya has begun enrolling followers in the southern province of Assiut, one of its main strongholds, in "popular committees" to maintain law and order, according to a senior leader of the group who spoke on condition of anonymity because of the sensitivity of the subject. The Islamist group supports Morsi.
Lists of volunteers with their addresses and phone numbers are being compiled there, he said. When activated, they will protect state installations, direct traffic and investigate complaints by residents, he claimed.
Before Gamaa Islamiya renounced violence, it played a key part in an anti-government insurgency in the 1990s. Now, it says the police strike and civil disobedience --like that seen recently in the coastal city of Port Said -- are part of a conspiracy to topple Morsi's administration.
The group has said it would send members of its "popular committees" to the streets if police abandon their duties. Hard-line Islamists have already branded police strikes as religiously prohibited amid calls for legislation outlawing the strikes.
"We are calling on anyone anywhere who is experiencing a security vacuum to fill it with popular efforts," Assem Abdel-Maged, a senior leader of the Gamaa, said on Monday.
Later the same night, hundreds of Gamaa members toured the city of Assiut on motorbikes, assuring residents through loudspeakers that the group was capable of ensuring security in the city and inviting Muslims and Christians to join the "popular committees." Christians account for some 35 percent of the population in Assiut province.
A joint statement signed by 15 Islamist groups, including the Gamaa and the Brotherhood, said that they "valued" the role played by "honest policemen" and are opposed to any attempt to politicize the force.
They warned against any attempt to destabilize the country, calling on all political forces to support the police "by all possible means, including popular committees if need be."
Egypt's security woes date back to the days of the uprising against Mubarak, which was sparked in part by hatred for the police force over years of abuse of power and brutality.
The force melted away after the revolution's deadliest day of clashes on Jan. 28, 2011 and police have since returned to work. But police have yet to fully take back the streets.
The security vacuum exacerbated by the striking police and violence in the heart of Cairo on Saturday appeared to be fueling the calls for creating popular committees to aid in policing.
Thousands of angry soccer fans rampaged through the heart of the capital on Saturday, attacking and setting ablaze the headquarters of the national soccer federation after they torched a police club.
The twin fires sent columns of thick black smoke billowing over the city of some 18 million. The fans were angered by the acquittal of seven of nine policemen tried for their alleged part in a soccer riot last year that killed 74 people.
Also, police pulled out from the coastal city of Port Said on Friday after days of deadly clashes with protesters who torched the security headquarters. The military is now in control of the city, which has been in open rebellion against Morsi's rule since late January.
On Sunday, drivers of Cairo's popular communal taxis staged a strike to protest fuel shortages, creating a traffic nightmare on the already congested streets of the city. Some of the drivers, armed with knives and guns, attacked others who did not observe the strike or got into fights with other motorists angered by their action.
The statement by the attorney general's office raised fears that it could provide legal cover for Morsi supporters to take on anti-government protesters.
The right of civilians to make citizen arrests is enshrined in a little known article in Egypt's penal code. The article says that such arrests should only be made when a citizen witnesses a crime that warrants holding the suspect in police custody in the run-up to a trial.
That condition, according to lawyer and rights activist Mohsen Bahnasi, assumes familiarity with the law by ordinary civilians.
"This statement paves the way for the creation of militias at a time when the country is going through a difficult transition," he said.
Associated Press writer Amir Makar in Cairo and Mamdouh Thabet in Assiut contributed to this report.