Gaza flotilla organizers said on Monday that Israel is pressuring Greece to halt the ships' departure.
American activist Ann Wright told a news conference that Israel is mounting a"tremendous diplomatic offensive" to prevent the flotilla from setting sail.
Organizers urged the Greek government in a statement not to "become complicit in Israel's illegal actions by succumbing to this pressure."
Organizer Vangelis Pissias said the flotilla is ready to leave in a few days, but gave no specific departure date.
Prime Minister Benjamin Netanyahu's inner cabinet on Monday instructed the Israel Defense Forces to be firm in preventing the flotilla from reaching the Gaza Strip while operating with maximal restraint to avoid causing injuries.
The senior government ministers also instructed the Foreign Ministry to continue its diplomatic efforts to prevent the flotilla from setting sail to Gaza.
Monday marked the second day of discussions by senior ministers on the planned Gaza flotilla. On Sunday, Netanyahu told the inner cabinet that Israel would not allow any ships to breach its maritime blockade of Gaza.
Security officials and Foreign Ministry representatives informed the cabinet on Sunday that Israel has no information indicating that terrorists or anyone affiliated with a terror group is planning to take part in the flotilla, said a government source. Nonetheless, there may be clashes between Israeli forces and some Arab activists aboard the ships.
"The critical mass of participants will include human rights activists from European Union countries, Canada and the United States," said a senior security official.
Some 10 ships are planning to set sail on Tuesday in an attempt to breach Israel's blockade of the Strip. The government and army are hoping the ships will stop on their own, possibly early Thursday, and that the Israel Navy will not have to board them, a move that would not be well received in the world.
Some 500 people are expected to be aboard the flotilla, which will include six or seven ships currently docked in Greece.
Assuming the ships do sail from Greece, they will meet up with two or three that have already set sail from Spain and France, and continue toward the Gaza coast.
The announcement two weeks ago from the Turkish group IHH that the Mavi Marmara ship will not take part in the flotilla has changed the security establishment's views regarding the anticipated resistance. IHH members violently resisted the naval takeover of the Mavi Marmara in the flotilla of May 2010, and nine of them were killed in the clashes. In addition, since the Mavi Marmara won't be part of this flotilla, only smaller ships will be involved, increasing the likelihood that Israel will not have to board them to force them to turn back.
Cabinet ministers were told on Sunday that after IHH announced that the Mavi Marmara would not be in the flotilla, there was less reason for concern about possible violent confrontations.
Government and defense sources said the fact that most, if not all, the flotilla participants will be European peace activists presumably not interested in violence will present a "more difficult public diplomacy challenge," and Israel wants to avoid clashes with the activists.
In contrast to the decision last year to deploy naval commandos onboard the ships when they ignored Israeli warnings not to continue to Gaza - this year Israel will try other methods to stop the ships and direct them toward Egypt's El Arish port.
The navy has, however, trained for scenarios involving violent resistance and forcible takeover of the ships, but this is considered a last resort. In such a case, the ships and passengers will be brought to a special security area at Ashdod Port.
"The IDF is preparing for all possible scenarios," the army spokesman said.
Flotilla organizers have been informed that if they dock first at Ashdod, Israel will bring the humanitarian aid directly to Gaza, a government source in Jerusalem said.
Israel has also talked in recent days with the interim government in Egypt, which has agreed to allow the ships to unload goods in El Arish, from where they would be sent to Gaza.
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