Haniya said these talks should be held "on the basis of no loser and no winner, and on the basis of no harm to anyone, and on the basis of a national unity government," his office said.
The United States and Israel want to isolate Hamas economically, diplomatically and militarily in the Gaza Strip, where armed factional clashes left the group in complete control just over a week ago.
At the same time, the US and Israel want to bolster the emergency government set up by Abbas in the Israeli-occupied West Bank after he dismissed the unity cabinet led by Hamas.
Hamas won parliamentary elections 18 months ago, but its government was shunned and heavily sanctioned by Israel and Western powers for refusing to renounce a right to violence against Israel and officially recognise the Jewish state.
Abbas is due to meet Ehud Olmert, the Israeli prime minister, in Egypt on Monday, but Israel has played down expectations of any immediate, tangible result.
Egyptian and Jordanian leaders will join them at the Red Sea resort of Sharm el-Sheikh to discuss prospects for resuming peace talks that have been effectively stalled for seven years.
Haniya has said Fatah will not be able to exclude Hamas when determining the future of the Palestinian people and insists that it, not Abbas's emergency cabinet, is the legitimate Palestinian government.