The Israeli navy is monitoring the vessel's progress and preparing to intervene if it continues on a course to Gaza.
"I say very clearly, no ship will arrive in Gaza. We will not permit our sovereignty to be harmed," the foreign minister, Avigdor Lieberman, said in a radio broadcast.
The ship, Amalthea, sailed from Greece at the weekend. It is carrying up to 15 activists and 2,000 tonnes of food and medicine, according to the organisers, a charity chaired by a son of the Libyan leader, Muammar Gaddafi.
The new attempt to break the naval blockade of Gaza comes six weeks after the Israeli navy's lethal interception of a flotilla, in which nine Turkish activists were killed. The assault prompted a wave of international condemnation and resulted in Israel agreeing to ease its blockade of Gaza.
However, it is strictly maintaining its sea blockade, saying it fears that any relaxation could lead to arms being shipped to militants in Gaza.
The Amalthea's captain was quoted as saying: "I haven't received any instructions to change the ship's original course. I am sailing to Gaza." The crew were expecting to reach Gaza on Wednesday.
"We hope the Israelis will not ban the ship from entering the port of Gaza," Youssef Sawani, director of the Libyan charity organising the trip, told Reuters.
"If they decide to do so we have no means to object to that. This is a peaceful mission. Our sole goal and intention is to have the goods delivered to those who need it. It is not to make an event or a show in high seas."
Israel has made intense diplomatic efforts to ensure the Amalthea does not approach Gaza.
Greece, from where the boat sailed, Moldova, under whose flag the boat is operating, and Egypt all agreed the Amalthea should be directed to El-Arish in Egypt, where its cargo would be unloaded, inspected and transferred to Gaza, Israeli officials said.
Gabriela Shalev, Israel's ambassador to the United Nations, wrote to the secretary general Ban Ki-moon, saying: "This mission is completely unwarranted ... We are deeply concerned that the true nature of its actions remains dubious."
She urged the international community to exert influence on Libya "to prevent the ship from departing to the Gaza Strip".
A spokesman for the Israeli foreign ministry said: "We are concerned about another political provocation. Libya is not a country that is heading efforts to protect human rights."
Israel claims it has the right under international law to prevent ships violating its naval blockade on Gaza.
The Israeli military is keen to avoid another confrontation at sea. "Everyone hopes this will be dealt with diplomatically," a spokesman said.
An investigation into the 31 May assault on the flotilla, commissioned by the Israeli military, has been completed and non-classified excerpts are expected to be made public this week.
The inquiry, which was restricted to examining the military preparations for dealing with the flotilla, is expected to be critical of intelligence, planning and co-ordination.
A broader investigation, the Turkel commission – instigated by the Israeli government – has begun examining the circumstances surrounding the flotilla's interception, although it is not expected to report for several months.
Postmortems into the nine activists killed on board the Turkish ship, the Mavi Marmara, may be published this week. Initial reports suggested that some of the dead had multiple gunshot wounds.
The assault on the Mavi Marmara led to a serious breach in diplomatic relations between Israel and it regional ally, Turkey. The Ankara government has insisted on an apology and an international investigation, without which it has threatened to sever ties.
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