(CNN) -- The MV Rachel Corrie, a cargo ship loaded with humanitarian aid and bound for Gaza in defiance of an Israeli blockade, is on track to arrive there Saturday, according to the Free Gaza Movement.
The 19 people aboard the vessel -- which is owned by the Free Gaza Movement -- include activists and crew members who are determined to reach Gaza, passengers told CNN.
"We're not prepared to turn around," said Irish Nobel Peace Prize laureate Mairead Maguire, who is aboard the ship. "We are prepared to go straight to Gaza."
"We will stay within the international waters," said Maguire. "If Israel refuses that we get into Gaza and insists on boarding our boat, then we will sit down as non-violent activists. We will be very peaceful. We will not resist the Israeli navy coming aboard, arresting us and taking us by force to [the Israeli port city of ] Ashdod, but we will not turn around. We will keep going."
Organizers say the ship is carrying 550 tons of cement to help rebuild schools, homes and other buildings destroyed in Gaza.
Maguire said the ship is also carrying "tons" of writing materials donated by Norway, pharmaceuticals and medical equipment -- including wheelchairs donated by Scotland -- and toys.
Former Assistant U.N. Secretary-General Denis Halliday, also aboard the Rachel Corrie, said the passengers had no plans to confront the Israelis.
"We will stand back and show we are harmless and unarmed -- we will put up no resistance," he said. "We're not going to make any silly mistakes."
Israel has offered to unload the vessel's cargo in Ashdod, screen the material and deliver it to Gaza, but passengers aboard the ship rejected the offer, according to a statement from Micheal Martin, Ireland's minister for foreign affairs.
Israel said its naval blockade is in place to stop weaponry from reaching militants in Gaza intent on attacking Israel.
"If, as is their stated intention, the Israeli government intercepts the Rachel Corrie, the government demands that it demonstrate every restraint," said Martin. He called on Israel to lift its blockade.
In Washington, National Security Council Spokesman Mike Hammer urged the passengers to accept Israel's offer.
"In the interest of the safety of all involved, and the safe transmission of assistance to the people of Gaza, we strongly encourage those on board the Rachel Corrie and other vessels to sail to Ashdod to deliver their materials to Gaza," Hammer said. He called on all parties "to avoid any unnecessary confrontations and to ensure the safety of all involved."
In an incident Monday, violence erupted on one of six ships in a flotilla carrying humanitarian aid to Gaza, leading to the deaths of nine people, all Turkish citizens -- including one of dual Turkish-American nationality. A number of other people were wounded.
Israel said the passengers initiated the attack; the passengers said it was the troops who initiated it.
On Friday, two Turkish ambulance planes left for Israel to carry five wounded Turkish citizens back to Turkey, the country's state-run Anadolu news agency reported.
Other Turkish activists on the ship have returned from Israel to a hero's welcome.
Turkish President Abdullah Gul said Thursday that the incident "left an irreparable and deep scar" in once-close Turkish-Israeli ties.
On Friday, thousands of people attended a funeral for the victims in Istanbul. Many of the attendees chanted anti-Israeli slogans.
Tensions among Palestinians are also simmering. "Ongoing provocations and systematic discrimination against Palestinians signify Israel's continuous disrespect of international law and human rights and destabilize the region," chief Palestinian negotiator Saeb Erakat said Friday.
The tensions have sparked security concerns within Israel. Israeli police spokesman Micky Rosenfeld told CNN a heightened police presence would keep the peace. Men under age 40 are not allowed to pray at the Al-Aqsa mosque in Jerusalem, he said.
The violence sparked official and grassroots rage in governments and streets outside the Middle East on Thursday. South Africa recalled its ambassador to Israel.
At the United Nations, the Security Council called for an inquiry into the flotilla raid and the Human Rights Council voted for a probe, but Israel said it alone -- and not an international entity -- should be investigating.
It is Israel's "standard practice" to carry out "a prompt, professional, transparent and objective investigation in accordance with the highest international standards" after military operations, said Mark Regev, a spokesman for the Israeli prime minister.
The Israel Defense Forces military advocate general -- charged with ensuring the military upholds the rule of law -- said Israel's interception of the flotilla was legal.
It said international law allows a country to stop a vessel in international waters if it attempts to breach a naval blockade -- even before such a blockade is breached.
Free Gaza activist Derek Graham has said the plan was for the Rachel Corrie to be unloaded in Gaza and then return to Ireland. "We're just hopeful the Israelis will let us make a small gesture for the people of Palestine," Halliday said. "Because we believe Monday was a gross error."
He added that Monday's confrontation resulted from "faults on both sides," saying the effort on the Rachel Corrie is a "different ball game."
The ship was named for a 23-year-old American woman who was killed in Gaza in 2003 while attempting to keep IDF forces from bulldozing the home of a Palestinian.
CNN's Ivan Watson, Paula Hancocks and Laura P. Maestro contributed to this report.