The entrance of the State House and some vehicles within the premises were vandalised by the angry residents.
According to reports, the groups picketed at various spots including the Parliament House, State House, AMA office and the Agbogbloshie Market.
According to a report on Citi FM, the demonstrators numbering about 200 entered the State House to draw the attention of the President to their plight as a result of the demolition which has left them homeless.
Another group, numbering about 1000 blocked the roads leading to the Agbogbloshie Market with burning tyres.
The Accra Metropolitan Authority (AMA) last Saturday demolished hundreds of structures at Sodom and Gomorrah, rendering scores of people homeless.
A taskforce from the Accra Metropolitan Assembly, with support from the security services are expected to take earth moving equipment to the area to demolish structures which for years have served as homes for thousands of migrants mostly from the Northern Region.
The threat to demolish follows the June 3 twin flood and fire disaster which claimed about 159 lives.