Their last meeting in Damascus on January 21 ended without a breakthrough and was followed by a surge in factional violence in which 63 Palestinians have died since January 25.
In the televised speech, Meshaal said: "I call on all our brothers ... to restrain themselves and to remember our real battle [with Israel]."
"It is pitiful to witness the bloody scenes in Gaza between the brothers"
Meshaal called on "all involved in the Palestinian arena, including Hamas and Fatah, to shoulder their responsibilities by putting an end to the bloodshed, and turn a new page".
He said: "We want a permanent calm, not a temporary one.
"Our real and only battle should be aimed against the occupation, against the separation wall, defending al-Quds [Jerusalem] and our Muslim and Christian holy sites.
"Our battle is to release 11,000 prisoners, our battle is against the settlement, our battle is for the right of return, self-determination and implementation of our national project."
Haniya to attend
Mohammad al-Madhoun, an aide to Ismail Haniya, the Palestinian prime minister from Hamas, said Haniya is also expected to attend Tuesday's talks.
Hamas and Fatah have tried in vain for months to agree on a national unity government, in the hope of ending a boycott by the US and EU.
Washington and Brussels consider Hamas to be a terrorist group and suspended direct financial aid to the Palestinians when the current Hamas-led cabinet took power last March.