Miri Eisin, a spokeswoman for the Israeli government, told Al Jazeera that the ship was boarded by soldiers at the edge of the maritime zone of Gaza in agreement with those on board.
"The people on board will be taken care off in accordance with Israeli law, as they have approached Israel illegally, so they will be asked to leave voluntarily," she said, adding the cargo would be off-loaded at Ashdod and then transferred to Gaza.
But Renee Jaouadi, a spokeswoman for the Free Gaza Movement that sent the aid ship, told Al Jazeera that they had made it very clear that they would not comply with Israel, "because their demands are against international humanitarian concerns".
"We did not want to take our cargo anywhere near Israel, we wanted to go directly to the port of Gaza," she said.
"If this boat has been boarded, it has been boarded illegally yet again."
Mukhriz Mahathir, head of the Perdana Global Peace Organisation, a Malaysian non-governmental organisation that sponsored the Rachel Corrie, said people would be willing to contribute to further aid ships.
"These actions have finally succeded in raising lots of awareness," he said.
"But for the moment, we are upset that these aid goods have not reached their destination."
Pro-Palestinian activists had earlier said they were determined to press ahead towards the Gaza coast, despite the Israeli warnings.
"We are not afraid and we are all advocating non-violence… and we will just sit here and go if they insist on commandeering our boat and forcing us into Ashdod," Mairead Maguire, an activist and Nobel Peace laureate aboard Rachel Corrie, said before radio contact with the ship was lost.
The Israeli military had warned that troops would consider storming the ship, if it continued its journey towards Gaza.
In a statement, the Israel navy warned the ship that it was "approaching an area of hostilities which is under a naval blockade. The Gaza area, coastal region and Gaza Harbour are closed to all maritime traffic."
Avital Leibovich, an Israeli military spokeswoman, told Al Jazeera that the military had a government directive to make sure the ship does not reach Gaza.
Al Jazeera's Nicole Johnston, reporting from Gaza, said the ship had hundreds of tonnes of aid, including medical supplies, wheelchairs, cement, building materials and even note-pads for children.
Dennis Halliday, the former UN assistant secretary-general who is also on board the ship, said on Friday that they expected Israeli military to intercept them.
"The current arrangements are unsustainable and must be changed. For now, we call on all parties to join us in encouraging responsible decisions by all sides to avoid any unnecessary confrontations"
Mike Hammer, White House national security council spokesman
"The cargo was checked three times - by trade unions in Ireland, by a member of the Irish senate, as well as Irish customs at the port," Halliday said.
"The cargo is sealed and we can't even access it ourselves," he said, explaining why they refused to take the ship to Ashdod.
The ship, carrying 11 activists and eight crew members, is named after an American womanwho was killed by an Israeli military bulldozer in the Gaza Strip in 2003, while trying to protest a house demolition.
Meanwhile in Washington the US said Israel's blockade on Gaza was unsustainable.
"We are working urgently with Israel, the Palestinian Authority, and other international partners to develop new procedures for delivering more goods and assistance to Gaza," Mike Hammer, a spokesman for the White House National Security Council, said.
"The current arrangements are unsustainable and must be changed. For now, we call on all parties to join us in encouraging responsible decisions by all sides to avoid any unnecessary confrontations," Hammer said in a statement.
"It remains a US priority to provide assistance to the people of Gaza," Hammer said.
"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, referring to the Israeli port.