The Fatah-allied president largely controls the occupied West Bank whereas Hamas runs the Gaza Strip.
In an exclusive interview with Al Jazeera, Ismail Haniya, the deposed Palestinian prime minister, said Fatah must stop arresting Hamas members in the West Bank before his group will join the talks.
"The campaign launched by the security forces in West Bank must come to an end," he said.
"All the political detainees in West Bank [must] be released and ... a delegation from the West Bank must join the Cairo talks."
Palestinian in-fighting
He also said some changes needed to be made to a reconciliation proposal put forward by Egypt, including that the two parties be treated as "partners standing on equal footing".
"If the three requirements are fulfilled, we will be ready for the internal dialogue, since our decision is built on the national interest and our desire to make this dialogue a success," Haniya said.
Abbas has accused Hamas of obstructing the talks under "false pretences", according to the Palestian MAAN news agency, saying "As if I was the one deciding who can leave the country!"
He said certain Fatah leaders have been unable to travel to Cairo due to Israel's border restrictions on the West Bank.
According to diplomats at the meeting in Cairo, Abbas is pressuring Arab countries to punish Hamas for its refusal to give up control of Gaza.
But they say no consensus has yet been formed and some countries, such as Qatar and Syria, favour a softer approach to accommodate Hamas.
Israeli blockade
Israel's siege of the Gaza Strip also featured high on the agenda of Wednesday's meeting.
Syria has proposed plans should be discussed to end the economic blockade imposed by Israel over Palestinian cross-border rocket fire.
Israel has largely kept Gaza's borders closed since Hamas took control of the Gaza Strip in June 2006 following violent clashes with Palestinian Authority security forces.
Three of Gaza's six border crossings were, however, opened for a few hours on Wednesday.
Lorries carried wheat, petrol and cooking gas, as well as humanitarian supplies from the the UN relief agency into the Palestinian territory.
A boat laden with food, medicine and other vital supplies also departed for the Palestinian coastal enclave on Wednesday morning from the Libyan port of Zawara, Jamal Khoudari, an independent legislator in Gaza, said.
Israel has said the blockade of Gaza will continue until Palestinian fighters stop firing rockets at Israeli towns.