The flotilla, organized by a pro-Palestinian activist group, consists of eight ships and carries 10,000 tons of medical equipment, housing material and other supplies.
Israel has criticized the activists for what it says is a propaganda stunt, while Turkey urged Israeli authorities to treat the convoy as humanitarian aid. One of the largest vessels in the convoy is chartered by a Turkish human rights group.
On Friday, a group of activists tried to leave Cyprus on smaller vessels to meet the larger convoy in international waters but was turned back by the authorities.
"Anything related to the trip to Gaza is not permitted," said Cyprus police spokesman Michalis Katsounotos.
A spokesman for the group said the activists, including 17 members of Parliament from Ireland, Bulgaria and Sweden, would attempt to meet the flotilla by departing through northern Cyprus, a breakaway Turkish Cypriot state.
"We are bitterly disappointed with the Cypriot government," said Greta Berlin, a spokeswoman for Free Gaza Movement, the group spearheading the effort.
Israel and Egypt closed Gaza's borders after Hamas took control of the territory in 2007 and refused to forswear violence against the Jewish state. Gaza's 1.5 million people face shortages of water and medicine.
Israel has said it would prevent the convoy from entering Gaza. Cyprus, an island in northeast Mediterranean, has been in the past used as a launch pad by activists headed for Gaza.
"We won't begin leaving until Saturday but the boats are still going," Audrey Bomse of the Free Gaza Movement said. "We've changed the coordinates twice because reportedly Israel has threatened to capture the Turkish ship so we decided to delay getting all the boats together," she added.
