The Sea Watch 3 vessel has made requests to several countries, a spokesman said, and Italy and Malta have refused with the weather worsening.
A civilian ship holding 33 migrants rescued off the Libyan coast appealed Sunday for a European port to take them in before the weather turns treacherous at Christmas.
The German non-profit ship Sea Watch 3 rescued the migrants, including four women and six children who were attempting the perilous journey across the Mediterranean Sea Saturday.
"We have requested a port of safety to disembark those people," Sea Watch spokesman Ruben Neugebauer told AFP. "There is no country willing so far to offer the people safe port." "We will try everything to get a port of safety before Christmas, because on the 25th the weather is worsening, so we urge European states to find a solution within the next 24 hours," Neugebauer said.
The rescued migrants include people from Nigeria, Libya and the Ivory Coast.
A Spanish civilian rescue ship with over 300 rescued migrants also off the coast of Libya was authorized Saturday to sail to Spain after Malta and Italy declined to let it come to port.
A newborn baby and his mother were airlifted from the ship operated by Proactiva Open Arms to safety in Malta.
Sea Watch said that they had attempted to contact the Libyan search and rescue coordination center but with no response.
More than 1,300 migrants have perished trying to reach Italy or Malta since the beginning of the year, according to the International Organization for Migration.
Aid groups have been sending rescue vessels into these waters despite vocal opposition from some leaders including Italy's far-right Interior Minister Matteo Salvini.
Accusing the groups of acting as a "taxi service" for migrants, he has denied them access to Italy's ports. Malta too has been increasingly unwilling to host rescue vessels.
A United Nations report Thursday said that migrants and refugees are subjected to "unimaginable horrors" from the moment they enter Libya, headed for the Mediterranean and Europe.
The climate of lawlessness in Libya provides fertile ground for illicit activities, leaving migrants and refugees "at the mercy of countless predators who view them as commodities to be exploited and extorted," the report said.
A majority of women and older teenage girls report having been gang-raped by men they cross paths with, the report said.