Abbas said: "We have to bring down this bunch, which took over Gaza with armed force, and is abusing the sufferings and pains of our people."
An Abbas aide said the president was not calling for a popular revolt against the group, rather reacting passionately to the bloodshed in Gaza City.
Hamas condemned Abbas's comments and accused him of selling out the Palestinian people in peace talks with Israel.
A formal relaunching of negotiations is set to take place later this month at a US-sponsored summit that is also meant to bolster Abbas in his struggle with Hamas.
Abbas's call for overthrowing Hamas coincides with his efforts to bridge differences with Israel ahead of the summit in Annapolis, Maryland.