The order, issued by President Mohamed Mursi on Sunday night, means the armed forces can detain people and refer them to prosecutors.
It says the military will support police to protect vital institutions until the results of a constitutional referendum planned for Saturday are declared.
Protests and violence have racked Egypt since Mr Mursi gave himself extraordinary powers last month. He claimed the move was necessary to speed up the transition to democratic rule since former president Hosni Mubarak's fall 22 months ago.
The president, bruised by the political uproar in which protesters have demanded his downfall, has rescinded the decree – although decisions made under it will remain in force.
However, his new edict, despite its limited nature, will revive memories of Mubarak's emergency law – also introduced as a temporary expedient – under which military or state security courts tried thousands of political dissidents.
A cabinet source said ministers had reviewed the decree last week, saying troops had secured elections during a military-run transition after Mubarak but, with a civilian president in charge, now needed a decree to allow them to play that role.
The new constitution is seen by Mr Mursi's Muslim Brotherhood party as a triumph for democracy and by its liberal foes as a religious straitjacket.
Opposition groups have called for mass protests today, saying Mr Mursi's eagerness to push the constitution through could lead to violent confrontation. They contest the legitimacy of the vote and of the process by which the constitution was drafted in an Islamist-led assembly from which their representatives withdrew.
They claim the document invites Muslim clerics to influence lawmaking and fails to embrace the diversity of 83 million Egyptians, one-tenth of whom are Christians.
Islamist groups have also urged their followers to turn out "in millions" today to show support for the president and for a referendum they feel sure of winning with their loyal base and perhaps with the votes of many Egyptians weary of turmoil.
The growing street protests prompted the army to step into the conflict last week, telling all sides to resolve their disputes via dialogue and warning it would not allow Egypt to enter a "dark tunnel". So far the military and the police have taken a relatively passive role.
Last night a military source insisted the new edict did not herald a move by the army to retake control of Egypt. He said: "The latest law giving the armed forces the right to arrest anyone involved in illegal actions, such as burning buildings or damaging public sites, is to ensure security during the referendum only."
Whatever the outcome of Saturday's referendum, the crisis has polarised Egypt and presages more instability at a time when Mr Mursi needs to enact tough policies to steady a fragile economy.
With the political crisis heating the streets, he suspended tax increases yesterday – only hours after the measures had been officially enacted – casting doubts on the government's ability to push through tough economic reforms that form part of a proposed $4.8 billion (£3bn) IMF loan agreement.
Mr Mursi is to visit the United States next year, although no precise date has been announced. The US gives Egypt about $1.3bn a year in military aid to bolster the peace treaty Cairo signed with Israel in 1979.
Mubarak, a close US ally, upheld the treaty for 30 years until he was overthrown in a popular revolt in February 2011.
Mr Mursi has said he will honour Egypt's treaty obligations, although some in the Muslim Brotherhood want the pact with Israel to be reviewed.