The group ate in the building opposite St Peter's Basilica and spoke to the pope about their new lives in Italy.
Vatican Radio has reported that children gave the pontiff drawings and he gave them toys.
The group of refugee families came over to Rome with Pope Francis after his visit to Lesbos, Greece, in April.
The Syrian group came over on two planes, the first with Pope Francis on his papal plane and the second later in June.
Other Vatican officials also joined the lunch and chatted with the families and played with the children.