Francesco Patton, whose custody of Catholic sites in the Holy Land covers shrines in Syria, and Michael Perry, minister general of the Order of Friars Minor, made the appeal in a joint statement.
"We ask that the entire international community take concrete steps to designate Aleppo a safe zone," they said.
"A safe zone surrounding Aleppo would allow the whole population, worn down by the terrible effects of the conflict, to receive essential humanitarian aid without discrimination, to find safety and security, and to recover some trust and hope in a speedy solution, which would be motivated by peace alone," they added.
Their plea came as Syrian regime forces advanced against rebels in the northern city during intense street battles on Tuesday, after the United States abandoned talks with Russia aimed at securing a truce.
Signup to our newsletter and follow us on Facebook and Twitter!
Patton and Perry said safe zones should be placed under the control of UN peacekeepers and operate "under a (UN) Security Council mandate with the full cooperation of the various parties involved in the war".
They also urged nations across the world "to be as generous as possible in accepting Syrian refugees".
The custody of the Holy Land is made up of 285 members of the Franciscan Order from 39 countries.
Its territory covers Israel, the Palestinian territories, Lebanon, Syria, Jordan, Cyprus, the Greek island of Rhodes and the monastery of Mosky in Cairo.