The pontiff's message came as he met survivors of the Lampedusa disaster, in which more than 350 migrants were killed as their ship sank off the coast of Italy a year ago.
Fifty of the survivors are now travelling to Italy to try to start a national day of remembrance for victims at sea.
The Holy Father said: "I find it difficult to speak to you because I don't know what to say.
"I cannot express what I feel, because words are not enough to describe what you have suffered. This can only be contemplated in silence, with tears and by trying to find a way to be close to you.
"The lives of people who need to migrate is hard, and when there are tragedies on this journey of migration, it becomes even harder, and when the end for those who have managed to reach a safe harbour seems certain then other even harsher realities arise, very often doors are closed, and you do not know where to go.
"I ask all the men and women of Europe to open the doors of their hearts. Behind, there are memories, there is the homeland and there are the dead."
The survivors gifted Pope Francis with an iron sculpture of a bottle adrift at sea, which contained a family instead of a message inside.
A bill has already been presented to the Italian parliament proposing October 3rd as World Day in Memory of Victims at Sea.