"On the horizon we see shadows and dangers which worry humanity," he said in the wake of an increase in security around the Vatican amid fears Isis extremists may be plotting to attack the head of the Roman Catholic Church.
"As Christians we are called not to lose heart or be discouraged," Francis said in a new year's message to the police.
Security was tightened in Saint Peter's Square in September after intelligence services intercepted a possible plan to attack the Vatican.
Iraq's ambassador to the Holy See, Habib Al Sadr, at the time warned that "what has been declared by the self-declared Isis is clear. They want to kill the Pope. The threats against the Pope are credible."
Some worry Francis has made himself a target by speaking out against the Isis group and having the Holy See voice support for US air strikes in Iraq.
Italy's interior minister this month said police were on high alert in key locations across Rome and around the Vatican after the Paris attacks.