We have to bring down this bunch, which took over Gaza with armed force, and is abusing the sufferings and pains of our people," Abbas said in a speech.
Hamas seized power in Gaza in June after routing forces loyal to Abbas' Fatah movement during five days of fighting. Abbas' spoke just days after Hamas opened fire on a mass Fatah rally in Gaza this week. Eight civilians were killed and dozens were wounded in Fatah's strongest challenge to Hamas in Gaza since the takeover.
In the past, Abbas, who has set up a separate government in the West Bank, has not gone beyond demanding that Hamas apologize for overrunning Gaza and reverse the takeover. Abbas aides said he wasn't calling for an uprising, but used unprecedentedly strong language against the Hamas regime because he was so furious about the bloodshed at the demonstration.
In his speech, Abbas also lashed out against "the outlawed gangs affiliated with Hamas in Gaza City."
Despite Abbas' tough words Thursday, he wields little control over Gaza. And following Monday's rally, Hamas has taken new steps to shore up its rule.
Hamas rounded up more than 400 Fatah activists this week, and on Wednesday announced media restrictions and plans to curb public gatherings.
Hamas government spokesman Taher Nunu said Abbas was "divorced from reality."
"The divide can't be resolved that way, only through dialogue," he said.
Five months of Hamas rule and crushing international sanctions have taken a heavy toll on already impoverished Gaza, and the hardship helped to drive the Fatah rally, which drew 250,000 people. Still, the heavily armed, Iranian-backed Hamas remains entrenched.
Hamas continues to bring in millions in cash through smuggling tunnels under the Egypt-Gaza border, enough to pay salaries to 16,000 members of its security forces and government employees.
Gaza militants are also undeterred, and according to the Israeli army, have fired more than 1,200 rockets and mortars toward Israel since June.
In northern Gaza on Thursday, the Israeli army opened fire on a car carrying militants, killing two and wounding five, militants and a health official said. The Israeli army said ground forces struck a group of militants about to fire rockets toward Israeli towns.
Abbas' call for an upheaval in Gaza coincides with his efforts to bridge differences with Israel ahead of a high-profile summit in the U.S. this month.
The conference is aimed at relaunching peace talks and bolstering Abbas in his struggle with Hamas, which does not recognize his mandate to negotiate.
Abbas said in his speech that his government was "working relentlessly" to make the gathering a "decisive-launching pad" for establishing a Palestinian state.
But he demanded that Israel halt all settlement construction, release Palestinian prisoners, and end its assassinations of Palestinian wanted men.
Abbas spoke on the 19th anniversary of the Palestinians' declaration of independence at a meeting in Algeria.
The declaration has not brought about the establishment of a Palestinian state, but is regarded as important because it implicitly recognized Israel's right to exist.