It was unclear if the Moldovan-flagged boat, with 12 crew and up to 10 activists on board, would try to reach Gaza in defiance of the Israeli blockade or would go to the Egyptian port of El Arish.
A spokesman at the Greek Foreign Ministry said the ship would head for El Arish.
An official from ACA Shipping, which owns the ship, told Reuters ahead of the ship's departure: "The ship will leave in a few minutes for Gaza. If they don't let us reach there (Gaza) we will head to El Arish harbor in Egypt."
An Al-Jazeera reporter accompanying the Gaza aid vessel said, "This will be a long journey, but currently the direction is Gaza. We must keep in mind that it will be four days before the ship (reaches its destination)."
Contrary to earlier reports regarding an agreement to sail to El Arish in Egypt, the captain said the ship would continue on its original route towards Hamas-ruled Gaza.
A charity chaired by the Libyan Leader's son Saif al-Islam Gaddafi is organizing the trip and said the Amalthea, re-named Hope for the trip, carried some 2,000 tons of food and medicine and complied with international rules. The trip was expected to take between 70 and 80 hours.
Nine pro-Palestinian activists died in May when Israeli marines stormed a Turkish aid ship leading a Gaza-bound convoy, prompting an international outcry and a condemnation from the United Nations Security Council.
Israel said its soldiers were attacked with knives and sticks when they boarded the ship and acted in self-defense.
Israel said on Saturday it contacted Greek, Egyptian and Moldovan authorities to make sure the ship chartered by the Gaddafi International Charity and Development Foundation would not attempt to reach Gaza.
Its ambassador to the United Nations sent letters to UN Secretary-General Ban Ki-moon and the president of the UN General Assembly, Ali Treki of Libya.
"In spite of the stated intention of this mission, we are deeply concerned that the true nature of its actions remains dubious," Gabriela Shalev wrote. "This mission is completely unwarranted," she wrote, urging the international community to ensure that the ship "does not sail".
The organizers said the Moldova-flagged ship contained only food and medicine and complied with international rules. Supporters of the charity making the trips were mostly Libyans, they said, with also one Nigerian and a Moroccan. The crew includes Cubans, Haitians, Syrians and Indians.
Israel says its blockade of Gaza is necessary to stop arms and materials it fears could be used for military purposes from reaching Gaza's Hamas Islamist rulers.
The United Nations says the blockade has led to a humanitarian crisis for the territory's 1.5 million people, of whom about 1 million depend to some extent on regular supplies of UN and other foreign aid brought in overland after Israeli inspection.
Following the international outrage caused by its raid on the aid flotilla, Israel has announced steps to ease the blockade of the enclave and set up an inquiry into the incident.