The Ocean Viking, operated by a French NGO, had picked up more than 230 migrants at sea near the Libyan coast before spending weeks seeking a port to accept them.
France allowed the boat to dock at the southern port of Toulon on Friday after Rome denied it access.
The stand-off has inflamed a dispute over the way EU countries handle migration across the Mediterranean.
Cyprus, Greece, Italy and Malta on Saturday slammed the EU's system for managing migrant flows and called for the EU Commission to intervene.
They hit out at the "disappointing" results of previous EU commitments to a scheme that in its initial year would have seen 10,000 people relocated from the European countries they first reached.
"The mechanism is slow" and the figure of 10,000 relocations, which was not met, "represents only a very small part of the actual figure of irregular arrivals during this year", they said.
The Greek migration minister and the interior ministers of Cyprus, Italy and Malta made the comments in a joint statement issued in Rome.
These countries have argued for years in favour of a compulsory relocation system.
They said that as states where migrants first enter Europe, they bear "the most difficult burden in the management of migratory flows in the Mediterranean, in full respect of international obligations and EU rules".
And they pointed the finger at humanitarian NGOs, saying their "private vessels act in total autonomy from the competent state authorities".
The Ocean Viking vessel , run by SOS Mediterranee, left to undergo maintenance at another port after the migrants disembarked at Toulon, authorities said.
In a few weeks' time it is set to return to save more migrants in the Mediterranean.
French authorities said the last of the 230 passengers disembarked late Friday. Four others were evacuated by helicopter earlier in the week.
Of the passengers, 189 people -- including 23 women and 13 minors -- were taken to a holiday camp turned shelter on the Giens Peninsula some 20 kilometres (12 miles) from the military port of Toulon.
'I needed to be on dry land'
Among them was an 18-year-old from Pakistan, who clutched a binbag containing his only belongings. Imran -- a pseudonym -- said he had spent 21 days at sea and felt exhausted.
He wondered how long he would be able to stay in France.
"They haven't told us anything," he said.
"As long as we are no longer in Libya or at sea, I am fine with anything. I needed to be on dry land."
His most pressing concern, he said, was to let his family know he is still alive.
The shelter has been designated a special "international waiting zone" that is not part of French territory and from which the migrants are not allowed to leave until their request for asylum has been processed.
French authorities said all new arrivals had expressed the wish to seek asylum.
They will have to undergo security checks, including from French domestic intelligence, before they can be interviewed by the country's refugee agency, whose representatives were expected to arrive on Saturday.
Another passenger, the first let off the Ocean Viking on Friday, is being treated in a French hospital for poor health.
A total of 44 unaccompanied minors -- mostly "young teenagers" -- have been handed over to French social services and are not staying at the Giens shelter, local official Evence Richard said.
Of all the disembarked passengers, 175 are to leave France and head to 11 other countries.
Germany is to receive 80 of the migrants, while Bulgaria, Croatia, Finland, Ireland, Lithuania, Luxembourg, Malta, Norway, Portugal and Romania have also agreed to take in a share.
The Ocean Viking initially sought access to Italy's coast, which is closest to where the migrants were picked up, saying health and sanitary conditions onboard were rapidly worsening.
Italy refused, saying other nations needed to shoulder more of the burden for taking in the thousands of migrants trying to reach Europe from North Africa every year.
The UN's International Organization for Migration says 1,891 migrants have died or disappeared so far this year while trying to cross the Mediterranean in the hope of a better life in Europe.