Two charity vessels that have rescued 484 migrants over the past days were on Monday waiting to bring their passengers ashore to Italy or Malta.
The Ocean Viking, run by SOS Mediterranee, has picked up 407 people over five rescue operations since Friday.
Among them there are 152 minors, including 10 under the age of five, and 12 pregnant women.
In a statement, SOS Mediterranee said it had asked both Italian and Maltese authorities to offer a safe port for the disembarkation of the migrants.
A further 77 migrants are on board the Alan Kurdi, operated by German charity Sea-Eye.
Sea-Eye spokesman Gorden Isler said Malta has refused to take in the Alan Kurdi, saying it is already overrun with migrants, while Italy has not yet responded.
In recent months, Italy and Malta opened their ports to rescue boats only after securing agreements from other EU countries that they would take in some of the incoming migrants.