Abbas is seeking to hinder the Egyptian mediation efforts because of his objection to the inclusion of jailed Fatah leader Marwan Barghouti.
A Hamas delegation pushed for a prisoner swap with Israel, while warning "violations" of Jerusalem could cause situation to explode.
Palestinian Islamic Jihad called for kidnapping IDF soldiers to force Israel to release security prisoners.
It is widely believed that the Egyptians are leading efforts to secure a deal between Israel and Hamas.
Thanks to Egyptian pressure, Israel and Hamas might be close to a prisoner swap deal, which could lead to a long-term truce.
United Nations and Egyptian mediators have reportedly told Hamas that the issue of rebuilding the Gaza Strip should be linked to a prisoner exchange agreement with Israel.
Israeli security officials are also scheduled to arrive in Cairo to discuss the prisoner exchange issue.
The Hamas leader said that "in the coming days we will be witnessing a dialogue in Cairo with the aim of reaching agreements on the issues at hand."
Hamas is holding two Israeli civilians, Avera Mengistu and Hisham al-Sayed, who entered the Gaza Strip on their own, and the bodies of IDF soldiers Hadar Goldin and Oron Shaul, killed in 2014.