About 25 passengers and crew will travel on the ship "Saoirse" (Gaelic for freedom), one of 10 vessels that are trying to leaving the Greek port of Piraeus, near Athens, for the tiny Palestinian enclave.
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"I would call upon the Israeli government not to take any action that would in any way cause injury or harm (to those on the flotilla)," Kenny told the lower house of parliament.
"We are supportive of a situation where there are no similar activities as took place before where people lost their lives when Israeli forces went on board a ship on the last occasion."
In May last year Israeli marine commandos stormed the lead ship of a previous flotilla, killing nine Turkish nationals in a move condemned across the world.
Kenny said he had visited Gaza in the past to see the situation at first hand, but that while he respected the motives of participants, his government's advice was not to travel to Gaza while the Israeli naval blockade was in force.
Vessel allegedly sabotaged by Israel (Photo: EPA)
"I have every sympathy with the people of Gaza," Kenny said.
"I have been there, I have met with group leaders, I have met with professional people who have been unable to give of their best by being able to travel outside Gaza."
Kenny said the EU would continue to use diplomatic and political initiatives to restart Israeli-Palestinian talks.
On Monday, Israeli military spokeswoman Lieutenant Colonel Avital Leibovitz said there were "radical elements" among the activists participating in the sea convoy.
Nearly 300 pro-Palestinian activists from 22 countries including Canada, France, Greece, Ireland, Italy and Spain are set to join the flotilla. They have rejected claims that they will use violence against Israeli troops.
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