The migrants were being transferred to two Italian ships, one Coast Guard and one Navy, because of forecasts of deteriorating weather conditions along the route to Valencia, Spain, according to SOS Mediterranee spokeswoman Mathilde Auvillain.
"Given the boat's location, it is between Italy and Malta", he added.
But the decision to close ports was significant because it showed Italy's willingness to put up a stop sign closer to its border.
Now it's been announced that Aquarius will be joined by an Italian coastguard ship and a warship to help them make the journey to Valencia, which is likely to take at least three days.
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.More news: Intel's First Dedicated Graphics Cards to Launch in 2020
The Sea Watch met the Trenton and was asked to pick up the survivors and bodies, but the group refused to bring them on board without a written guarantee from Italy.
"In the Mediterranean.there's Malta that does now welcome anyone, there is France that rejects [refugees] at its borders, there's Spain that defends its borders with the arms".
EU rules mean migrants must apply for asylum in the European country where they first arrive, putting pressure on Italy and Greece, the entry points for hundreds of thousands of people fleeing war and poverty in the Middle East, Africa and Asia since 2015.
UNHCR also pointed to "key treaties" stating that a nation which has responsibility for an area in which a search-and-rescue operation takes place is required to "exercise primary responsibility" for coordinating the migrants' safe disembarkation.
Matteo Salvini, Italy's Interior Minister and Northern League party leader chose to refuse docking to "Aquarius" and redirect the vessel to the Island of Malta, apparently in line with his election promises.
In a statement late Sunday after speaking with his Italian counterpart, Mr Muscat refused to let the ship dock in a Maltese port, but said Malta would conduct emergency medical evacuations if necessary.More news: Google will ban inline extensions starting with Chrome 71
For those aboard the Aquarius, Spain's offer of docking rights at the port of Valencia was welcome news, although it did not provide a quick or easy solution.
The ship has enough water on board but would begin running out of food by this evening, he said.
Doctors Without Borders (MSF), which is operating the Aquarius alongside SOS Mediterranne, urged Rome to drop plans for the lengthy trip to Spain for its migrant passengers.
"Particularly seven pregnant woman, 15 with serious chemical burns and several critical drowning hypothermia patients", the NGO said.
"There are more than 600 people onboard, they are exhausted, they want to get to safety, there is, of course, a lot of tension among them because they are not sure what is going to happen", she added.
"Our objective is the disembarkation in a port of safety of the 629 people now on board the Aquarius - some we rescued yesterday night in hard conditions", she was quoted by Reuters as saying. The Aquarius picked up almost 630 migrants, including over 120 unaccompanied children and seven pregnant women on Saturday (09/06).More news: ‘Dumbo’ First Trailer: Tim Burton Brings Disney’s Lovable Elephant to Dazzling Life