It is the first meeting between Fatah leader Abbas and Meshaal, who heads the Hamas movement that rules Gaza, in almost a year, and is aimed at ending years of bitter rivalry between the two groups.
On their visit to Cairo, the two leaders are also holding separate meetings with Egypt’s Islamist President Mohammed Mursi.
Mursi’s Cairo office said Abbas and Meshaal will first “meet Egypt's intelligence chief before holding a three-way meeting with President Mursi,” AFP news agency quoted presidential spokesman Yasser Ali as saying.
The meeting will also be the first between Abbas and Meshaal hosted by the Egyptian president since he was elected in June 2011.
Azzam al-Ahmad, who is in charge of reconciliation efforts between his Fatah party, of which Abbas is head, said Abbas was traveling to Egypt at Mursi’s invitation to discuss the subject.
Meshaal and aides arrived in Cairo from Doha on Tuesday for a visit of several days, the official MENA news agency said.
Hamas and Fatah had been at loggerheads since the Islamist movement seized control of Gaza in June 2007, following its victory in Palestinian parliamentary elections the previous year.
Under Egyptian mediation, the two groups reached a unity agreement in April 2011, but the main provisions of that deal have so far not been implemented.
Egyptian officials have said that a reconciliation agreement that would allow Hamas representation in the umbrella Palestine Liberation Organization, historically headed by Fatah, and the formation of a unity government, are opposed by Washington.
The United States, along with other Western countries and Israel, say Hamas must renounce violence and recognize Israel.
Hamas is officially sworn to Israel’s destruction but says it could accept a Palestinian state on the basis of the lines which existed before the 1967 Six Day War during which the Jewish state captured the West Bank, Gaza Strip and east Jerusalem.