Hamas sources said Mashaal is expected to be chosen as the paramount leader of the group to replace Ismail Haniyeh, who was assassinated in Iran in the early hours of Wednesday.
"Go forth, light and heavy, and strive with your money and your lives in the path of God," the Hamas leader added.
Turkey was deliberately chosen as the site of the meeting, as it was deemed safe enough for the leaders to meet there.
Khaled Meshaal served as chairman of the political bureau of Hamas between 1996 and 2017.
Ex-Hamas chief Khaled Mashaal said Jordan, Syria, Lebanon, and Egypt have a bigger duty to support the Palestinians.