"There is another stage concerning the departure of the Israeli Army from the Gaza Strip expected to be completed on 4 October or it might be at any moment," Abbas said on Wednesday after meeting Egyptian President Hosni Mubarak in Cairo.
Abbas provided no further details on the departure.
The withdrawal of Israeli occupation forces is the final step in its departure from Gaza. Israel's army must destroy Jewish settlements and military bases before staging their own pullback.
Earlier on Wednesday, Israeli Defence Minister Shaul Mofaz said Israel and Egypt had reached an agreement to have 750 Egyptian troops take control of the Egypt-Gaza border area from departing Israeli occupation forces.
Egyptian border patrol
"This agreement ultimately gives comprehensive - and I emphasise comprehensive - responsibility to the Egyptians regarding the prevention of weapons smuggling in the Philadelphia corridor in tunnels and above ground, into the Gaza Strip," Mofaz told Israel's Army Radio.
It was not immediately clear what responsibilities Palestinian troops on the Gaza side of the border would have.
Palestinian forces have been working with Israeli troops along the border since a period of calm was agreed upon between Palestinian resistance movements and Israel earlier this year.