The Dignite/Al Karama left the Greek island of Kastellorizo late on Saturday following a troubled stay in Greece after Athens imposed a ban on the departure of any ships planning to join an international flotilla heading for Gaza.
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Reached by satellite phone on board the ship, activist Thomas Sommer-Houdeville said the lone vessel expected to reach Gaza on Tuesday afternoon.
"We hope to arrive between 12 and 2, we don't want to go during the night," he told AFP, adding that the yacht was carrying a "symbolic message of peace and hope and love."
Israel on Monday vowed to block any attempt to reach Gaza by sea. "If this boat is on its way to Gaza, which is a breach of international maritime law, and tries a provocative act, yes, we shall intercept it," Deputy Foreign Minister Danny Ayalon told reporters in Jerusalem.
"But I assure you we shall try our best to make those on board very comfortable."
Sommer-Houdeville said the activists on board the boat had no specific plan for how to respond if Israel tried to stop the vessel or board the yacht.
"We hope that they will not, we don't have a plan but we have a peaceful humanitarian mission. We are a peaceful boat flying a French flag," he said.
On board are 16 people, including three crew members and three journalists, among them Amira Hass, a veteran columnist with the left-leaning newspaper Haaretz.
The crew and seven of the passengers are French, while another three are representing boats which had been due to join the flotilla but were blocked from leaving Greece.
The French-flagged Dignite/Al Karama managed to sail past the Greek coastguard on July 5, but two days later was blocked by authorities in Crete when it stopped to refuel.
It sailed to Kastellorizo, which lies just off the coast of southwestern Turkey, on Thursday.
The boat and its activists were well received on the island, which has a population of more than 400 people, some of whom fled their homes during World War II and found temporary refugee in Gaza, organisers said.
Activists had hoped a 10-ship Freedom Flotilla would be able to sail from Greece to Gaza at the end of June, but the effort was hit by a wave of red tape and technical faults which organizers blamed on Israeli sabotage.
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