The Irish Government believes the Rachel Corrie should be allowed to reach Gaza, according to Minister for Foreign Affairs Micheál Martin.
He said the ship should be allowed to proceed to Gaza and unload its humanitarian cargo.
'If, as is their stated intention, the Israeli government intercepts the Rachel Corrie, the Government demands that it demonstrate every restraint.
'Those on board the Rachel Corrie have made clear their peaceful intentions and have stated that they will offer no resistance to Israeli forces.
'Based on these assurances, there can be no justification for the use of force against any person on board the Rachel Corrie.'
The Minister has been involved in efforts to strike an agreement between both sides, but that was declined by the activists on the vessel.
Mr Martin said he had reached agreement with the Israeli government to allow the vessel dock in the Israeli port of Ashdod.
The ship's cargo would have been unloaded and inspected under supervision from the UN and officials from his department. It would then have been transported to Gaza along with two activists.
In a statement Minister Martin said: 'In my view, such an arrangement would have offered a useful precedent for future humanitarian shipments, pending the complete lifting of the blockade.
'This proposal was put to those on board the Rachel Corrie who, on Friday afternoon, after careful consideration and having thanked the Government for its efforts, declined to accept it.
'I fully respect their right to do so and to continue their protest action by seeking to sail to Gaza.'
The Irish Palestinian Solidarity Campaign said the offer 'was unacceptable to those on the Rachel Corrie'.
Israel delivers message to Rachel Corrie
Israel earlier proposed that the ship sail to the port of Ashdod, where it would 'ensure that no weapons and or war material were on board.'
Israel's Foreign Ministry Director General Yossi Gal said this 'clear message' had been delivered to the MV Rachel Corrie.
'If the ship decides to sail to the port of Ashdod in Israel then we will ensure its safe arrival and will not board it,' he said.
Speaking on RTE's News At One, activist and Nobel Laureate Mairead Corrigan Maguire said the vessel was progressing to Gaza and was expected to arrive in the 25-mile exclusion zone at 6am Irish time tomorrow.
The IPSC said the vessel is now 100 miles from Gaza and will slow down through the night to avoid any confrontation in darkness.
Israel has rejected international calls for an outside investigation into its military raid on a flotilla of ships carrying aid for Gaza.
It said its military had already begun its own inquiry into last Monday's operation, in which nine activists were killed.
Turkey has sent two medical planes to Israel to bring back five of its nationals wounded during Israel's attack on the flotilla.
The five, all men, are the last Turkish pro-Palestinian activists still being held in Israel.
The bodies of the nine people killed - eight Turks and a US citizen of Turkish origin - were returned to Turkey yesterday, along with 19 wounded and 450 activists rounded up during the commando raid.