They were also concerned the vessel, which was built to transport just 500 people, could not safely carry all 629 of those rescued at sea.
But the Aquarius is heavily overcrowded, making the four-day trip to Spain particularly perilous.
While Spain adopted a diplomatic tone with Italy when it announced it would take the migrants, relations between Rome and Paris have deteriorated in an explosion of accusations and counter-accusations.
Spanish socialist Prime Minister Pedro Sanchez offered to allow the Aquarius to dock in Valencia, insisting it was an "obligation" to do so.
SOS Mediterranee tweeted late on Sunday that the Aquarius had "received instructions from the Italian Maritime Rescue Coordination Centre to standby in our current position which is 35 nautical miles from #Italy and 27 nautical miles from #Malta".
A little more than a week ago, Italy's new interior minister, Matteo Salvini, told a crowd that "Italy and Sicily can not be Europe's refugee camp" and "the good times for illegals are over", Deutsche Welle reports.
The Aquarius was denied the right to dock in Italy and Malta.
France has not pulled its punches over Sunday's decision by the new Italian interior minister, Matteo Salvini, who is also leader of the far-right League, to prevent a rescue ship operated by a French NGO from docking in Italy.
But a spokesman for Macron's Republic on the Move party said the Italian government's policy was "sickening".
Even as Italy worked to dispatch the charity ship, an Italian Coast Guard vessel with 937 migrants aboard was heading north from the Libyan coast and was expected to dock in Sicily on Wednesday.
"From now also Italy begins to say NO to the traffic of human beings, NO to the business of illegal immigration".
The question of where boats land is a critical one, because European rules require refugees to request asylum in the country where they first arrive.
"My aim is to guarantee a peaceful life for these youths in Africa and for our children in Italy", Mr Salvini said, using a Twitter hashtag which translates to, "We are shutting the ports".
Given that the aid ship had no emergency, Italy made a decision to appeal to other European countries "so they don't leave Italy alone yet again in managing the migratory flows, which is a phenomenon that is all of Europe's business", Di Maio said in a Facebook post.
The Aquarius is one of the few remaining non-profit rescue ships left in the central Mediterranean, where so far this year 784 migrants have drowned during the crossing, according to figures from the United Nations Refugee Agency.
MSF Sea (Doctors Without Borders) said the medical situation of those on board was "stable for now but unnecessary delay to disembarkation in safe port puts vulnerable patients at risk".
Italy had argued that Malta, a tiny island nation that also is an European Union member, was the safest, closest port to the ship.
It took six different operations by a French charity called SOS Mediterranee to pick up all 629 migrants and get them aboard a rescue ship called Aquarius.
"We call on all involved to contribute to a swift resolution so that the people on board the Aquarius vessel may be safely disembarked as soon as possible".