Mr Abbas said Hamas must respect his authority over Palestinians
Palestinian leader Mahmoud Abbas is due to meet Egypt's President Hosni Mubarak in Cairo, as part of efforts to bring about a long term ceasefire in Gaza.
Egypt has been mediating between Israel and Hamas, which controls Gaza, during the conflict in the coastal enclave.
Mr Abbas has accused Hamas of risking Palestinian lives and said its leaders must respect his authority.
The latest talks follow an upsurge in violence, with Israel carrying out air strikes in response to rocket attacks.
Cairo has been holding separate talks with Israeli officials and Palestinians from both Hamas and Mr Abbas's Fatah party, which runs the self-rule Palestinian Authority in the occupied West Bank.
Mr Mubarak wants to negotiate a permanent ceasefire which could lead to Gaza's borders being reopened after an 18-month Israeli blockade which has prevented all but the most basic humanitarian supplies from entering.
It would also bring an end to the smuggling of weapons through tunnels in the sandy soil underneath Egypt's borders into Gaza.
Representatives from Hamas are in Cairo, but Mr Abbas has said talks were impossible with anyone who rejected the supremacy of the Palestine Liberation Organisation, which he leads.
This follows a statement last week by the exiled leader of Hamas, Khaled Meshaal, said the PLO "expresses a state of impotence, abuse and a tool to deepen divisions". Hamas has never been a member of the PLO.
There has been a rift between Fatah and Hamas since Hamas took control of Gaza by force in mid-2007.
Mr Abbas has accused Hamas of having "taken risks with the blood of Palestinians, with their fate, and dreams and aspirations for an independent Palestinian state".
Separately, on Monday the UN relief agency Unrwa said Israel had stopped a convoy of 10 trucks carrying paper and educational materials for its schools in Gaza from entering the Strip.
Israel said Unrwa had not coordinated its attempt to bring in the supplies properly with the Israeli authorities.
The talks come after Israeli aircraft bombed a Hamas security target in Gaza City and tunnels used by the militant group along the border with Egypt.
There were no reports of casualties in Gaza following the attacks late on Sunday.
Israeli PM Ehud Olmert had earlier vowed a "disproportionate" response to rocket attacks on Israel from Gaza, after at least two rockets hit southern Israel, injuring two soldiers and a civilian.
The Israeli civilian casualty was the first since the 18 January ceasefires which ended Israel's three-week assault on Gaza, which it said was aimed at stopping rocket attacks.
Both Israel and Hamas have independently declared ceasefires, but they have been broken several times.
About 1,300 Palestinians and 10 Israeli soldiers were killed in Israel's devastating three-week assault on Gaza. About a third of the Palestinian dead and wounded were civilians, while three Israeli citizens died in rocket attacks.