In the past, the Palestinian leader, 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.
In his speech, Abbas lashed out against the outlawed gangs affiliated with Hamas in Gaza City, where forces loyal to the Islamic group opened fire on a mass rally by his Fatah movement on Monday. Eight civilians were killed and dozens were wounded in the strongest Fatah challenge to Hamas rule since the Hamas takeover.
Hamas also rounded up more than 400 Fatah activists, and on Wednesday announced media restrictions and plans to curb public gatherings.
Discontent in the strip is growing, in part because Israel's closure of Gaza's borders immediately after the Hamas takeover has shut down many factories, cost tens of thousands of jobs and driven up prices.
Hamas' efforts to cement its grip on Gaza coincides with efforts by Abbas and Israel to bridge differences 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.