It is hoped that the forming of such a government would lead to the lifting of a Western aid embargo, as well as trade restrictions imposed by Israel.
Abbas said in a speech marking the second anniversary of the death of Yasser Arafat: "I announce to our people the happy news that we have achieved great progress on the path to establishing a national unity government that can end the siege and open the way towards a political settlement.
"I expect that, God willing, this government will see the light of day before the end of this month."
He said that forming a coalition government would provide conditions for an end to economic sanctions imposed on the Hamas-led government.
Abbas used his speech to reiterate the Palestinians' claim for a state in the West Bank and Gaza, with east Jerusalem as its capital.
He said: "The Palestinian people will not concede any acre of its land, including Jerusalem."
The United States and Europe imposed sanctions on the Palestinian Authority after Hamas defeated Abbas's more moderate Fatah faction in January's elections.
"It is high time the Israeli government realises that the continuation of its settlement and occupation is an impossible matter and that military force, no matter how mighty, will not break the will of the people"
Mahmoud Abbas, Palestinian president and leader of Fatah
Israel also withheld tax and customs receipts owed to the Palestinians.
Hamas, continues to assert that it will not recognise Israel, yet Ismail Haniya, the Palestinian prime minister and leader of Hamas, said on Friday he was prepared to step down if it would bring an end to the embargo.
Israel has cautiously welcomed Abbas's efforts, though it insists that any new Palestinian government must recognise Israel's right to exist and renounce violence, before peace talks.
Tzipi Livni, the Israeli foreign minister, said on Friday: "There is hope for the moderates, those who believe in a two-state solution."
Abbas said Israel must also take responsibility.
He said: "It is high time the Israeli government realises that the continuation of its settlement and occupation is an impossible matter and that military force, no matter how mighty, will not break the will of the people."
Since Hamas's election victory in January there has been increasing violence between Israeli forces and Palestinian fighters.
There has also been fierce fighting between Hamas and Fatah loyalists.