There are 17 people on board the German Sea-Eye vessel, with another 32 on the Sea-Watch. Among them are a one-year-old baby and two children aged six and seven.
Pope Francis on Sunday urged EU leaders to show "concrete solidarity" with 49 migrants stranded on charity ships off the coast of Malta who have been refused permission to land.
With his comments in an address to 60,000 people in St. Peter's Square for the feast of the Epiphany, Francis jumped into a diplomatic fracas between Italy and Malta and into an internal dispute among leaders of Italy's populist government.
"I make a heartfelt appeal to European leaders to show concrete solidarity for these people," Francis said, raising his voice. They were only "seeking a safe port where they can disembark", he said.
"Forty nine migrants rescued in the Mediterranean by two NGO ships have been onboard for several days now, waiting to be able to disembark," Francis added. "I address a pressing appeal to European leaders that they show some concrete solidarity with respect to these people," he added.
Amid growing concern over the plight of the migrants, some of whom have been at sea for more than two weeks, the European Commission earlier this week called on EU member states to admit them.
The Netherlands and Germany have offered to take some but only if their EU partners do the same, highlighting again the European Union's long-running deadlock over sharing responsibility for migrants.
Both Italy and Malta have refused port access and on Sunday they reiterated that position.
"In Italy, there are no more arrivals. That is the line and it will not change," far-right Italian Interior Minister Matteo Salvini told the Il Messaggero newspaper. "Italian ports are closed and will remain so," he added in a tweet.
Italy and Malta are predominantly Catholic nations but the Church's influence in politics has waned significantly in recent years.