The Aquarius, run by Franco-German charity SOS Mediterranee and Doctors without Borders (MSF), picked up the migrants in two separate operations and is now in global waters between Italy and Malta.
SOS Mediterranee in a statement said that because of the recent refusal of Italy and Malta to let rescue vessels carrying migrants dock, ships might be now unwilling to get involved fearing they will be stranded with migrants aboard and denied a port to disembark them.
The vessel, which is jointly operated by MSF and SOS Mediterranee, is understood to have rescued the migrants on Friday.
Malta said it had no legal obligation to berth the ship and Spain said its ports were not the safest destination.
European Union border agency Frontex said on Monday it counted 73,500 "irregular border crossings" into the bloc so far this year via the sea and the Western Balkans route, more than 40 percent fewer than in the first seven months of 2017.
The Aquarius, one of the last two NGO vessels still operating in the central Mediterranean. was the first charity ship to be turned away from Italian ports in early June, before being taken in by Spain. "No more to human trafficking and their accomplices", he said.
Meanwhile, Italy's Transport minister Danilo Toninelli suggested the ship make its way to Gibraltar, since it was flying the British territory's flag. "At this point, the United Kingdom should take responsibility for the safeguarding of the shipwrecked", Toninelli wrote on Twitter.
Sky News has contacted the UK Home Office for comment.More news: Here's how to see the Perseid meteor shower this weekend
The European Commission was in touch with several EU states and trying to help resolve the situation, a spokesman in Brussels said.
The rubber dinghy was taking in water when it was found, however, all migrants were rescued by an AFM patrol vessel. The migrants will be brought to Malta in the afternoon, sources said.
Spain eventually agreed to take in the boat, but there was no indication of where the Aquarius might head on Sunday, with Malta immediately refusing it access and Italy saying at the weekend it would not be welcome at any of its ports.
On Monday SOS Mediterranee said it had reached a standby position "exactly between Malta and Italy and awaits to be assigned a place of safety".
An estimated 720 people died in June and July when charity ships were mainly absent, Amnesty International estimates.
"Aquarius is now standing by at 32 Nautical miles from the European coast", the ship's digital log said on Monday.
The Libyan JRCC informed the Aquarius that it would not provide a place of safety and instructed Aquarius to request a place of safety from another coordination centre.