The announcement came after security forces broke up two sit-in protests last week by those calling for the reinstatement of President Mohamed Morsi, the Brotherhood leader deposed in a coup last month.
The clashes killed more than 600 people and sparked protests and violence that resulted in the deaths of 173 individuals last Friday alone.
Cabinet spokesman Sherif Shawki said that the prime minister, Hazem el-Beblawi, who leads the military-backed government, had assigned the ministry of social solidarity to investigate the legal possibilities of dissolving the group.
The announcement came as a mosque in the country’s capital was evacuated following heavy gunfire. Protesters who had barricaded themselves inside were arrested by security forces.
Television images showed shots being exchanged between a gunman in the main minaret and security forces on the ground.
The Brotherhood is technically a banned organisation. It was officially dissolved by Egypt’s military rulers in 1954, but it recently registered itself as a non-governmental organisation.
If it was legally dissolved, its property and assets could be seized.
The Brotherhood has called for daily demonstrations since a crackdown on its protest camps in Cairo on Wednesday that left hundreds of its supporters dead.
The most recent standoff began early yesterday morning, when the al-Fath mosque – which was being used as a makeshift clinic for the injured and a morgue for the dead from Friday’s clashes – became transformed from a field hospital into a fortress.
Brotherhood members barricaded themselves inside the building, using anything at their disposal.
Before long it had become a scene of chaos. Tear gas was fired into the building, and witnesses saw live ammunition fired by both sides.
Al-Jazeera television contacted one woman inside the mosque on her mobile phone as the shooting began.
“Nobody here is safe, they are shooting inside the mosque,” she said. Loud firing could be heard in the background.
Egyptian police brought Morsi supporters out of the building – leading some, dragging others – but then found themselves having to protect them from angry mobs armed with bats and pieces of wood who were trying to attack them.
Separately, the Egyptian authorities said they have arrested the brother of the al-Qaeda leader Ayman al-Zawahiri.
Mohammed al-Zawahiri was detained at a checkpoint in Giza, near Cairo, because of his links to Morsi, according to security officials.
Also yesterday, the Muslim Brotherhood said on its Facebook page that Ammar Badie, the son of the movement’s spiritual leader, General Guide Mohamed Badie, was one of those killed during protests on Friday. He died of a bullet wound in Ramses Square.
His father was arrested after the removal of Morsi and charged with inciting violence.
It has not been revealed where he is being detained.
The secretary-general of the Brotherhood’s Freedom and Justice Party, Mohammed al-Beltagi, said his 17-year-old daughter, Asmaa, died in earlier protests.
The Muslim Brotherhood group, founded in 1928, came to power a year ago when Morsi was elected in the country’s first free presidential elections. The election came after the overthrow of the autocratic leader Hosni Mubarak in a popular uprising in 2011.
The fundamentalist group has been banned for most of its 80-year history and repeatedly subjected to crackdowns under Mubarak’s rule. While sometimes tolerated and its leaders part of the political process, members regularly faced long terms of imprisonment and arbitrary detentions.
Since Morsi was deposed in the popularly backed military coup, the Brotherhood has stepped up its confrontation with the new leadership, holding sit-ins in two encampments for weeks, rallying thousands and vowing not to leave until Morsi is reinstated.
In the most recent standoff, Egyptian security forces exchanged heavy gunfire yesterday with armed men at top of a minaret of a Cairo mosque.
The security forces fired tear gas, stormed the mosque and rounded up hundreds of Islamists supporters of Morsi who had been barricaded inside overnight.
The confrontations on Friday – around a Brotherhood call for a “Day of Rage” – killed at least 173 people, said Shawki, the cabinet spokesman. He said 1,330 people were wounded in the protests.
Egypt’s interior ministry said in a statement that a total of 1,004 Brotherhood members were detained in raids across the country and that weapons, bombs and ammunition were also confiscated.
In a separate incident in Libya yesterday, a small explosion rocked the Egyptian consulate in the city of Benghazi, blowing out its windows and those of adjacent buildings.
A policeman at the scene said an Egyptian security guard was injured in the explosion, apparently caused by a small bomb hidden in a briefcase. At least five cars were damaged.