Sisi is expected to resign as defence minister and army chief and announce his candidacy this week, following the interim president's approval of a law to organise the poll.
His supporters see him as the best suited leader to restore stability and law and order amid persistent militant attacks and street protests by Morsi's supporters.
In Saturday's attack, masked gunmen opened fire on military policemen as they were finishing their morning Muslim prayers and then planted two bombs to target first responders, the military said in a statement.
The health ministry said six soldiers were killed.
In an emergency meeting that ended early Sunday morning, the cabinet decided to "decisively confront whoever attacks citizens and civilian and government installations," it said in a statement.
It emphasised that attacks on the army would be dealt with by military courts, in accordance with a constitution approved in a referendum in January.
The government also ordered heightened security measures to counter what has become a low-level insurgency that has killed more 200 soldiers and policemen since Morsi's overthrow.
Most of the attacks since have been carried out in the Sinai, but militants have expanded their reach to the Nile Delta and the capital in recent months.
The government has mostly blamed Morsi's Muslim Brotherhood, which renounced violence decades ago and has denied any involvement.
The most prominent attacks, including a car bombing at a police headquarters in Cairo and the downing of a military helicopter in Sinai, have been claimed by Ansar Beit al-Maqdis (Partisans of Jerusalem), a Sinai-based jihadist movement.
The group said in a statement Friday that one of its founders, Tawfiq Mohamed Fareej, died last week when a car accident set off a bomb he was carrying.
Fareej led a 2011 cross-border attack in Israel that killed eight people and was also involved in a failed attempt on the life of Egypt's interior minister, it said.
The group has said the attacks in Egypt are in retaliation for a brutal government crackdown on Morsi's Islamist supporters, which Amnesty International says has claimed some 1,400 lives.
- Growing militancy -
Morsi won Egypt's first-ever democratic presidential election, following the 2011 uprising that ended Hosni Mubarak's three-decade rule.
But his year in power bitterly polarised Egyptians, and the military ousted him amid mass protests demanding his overthrow.
Since his ouster and subsequent arrest, his supporters have staged weekly rallies that often set off deadly clashes with security forces and Morsi opponents.
Meanwhile, the army has poured troops and armour into the lawless Sinai to combat the growing militancy, often targeting suspected gunmen with air strikes.
Analysts say the army campaign has led the jihadist militants in Sinai, some inspired by Al-Qaeda, to adapt by staging less frequent but more widespread attacks across the country.
With the Brotherhood decapitated by the crackdown, some of its members might also have decided to form militant cells to target policemen, they say.
Morsi, who is still in jail, faces three separate trials for involvement in the killing of opposition protesters and collusion with militants to carry out attacks in Egypt.