Declan Lang, who also speaks on international affairs on behalf of the Catholic bishops of England and Wales is raising concern in a week which has seen an estimated 141 people killed including 18 children.
The Syrian Observatory of Human Rights is reporting hundreds of injuries as a result of Russian and Syrian air strikes and shelling by government forces and its allies on the besieged city.
"We are shocked and horrified at the violent attack on civilian lives, especially women and children, in East Aleppo," said Bishop Lang.
"The destruction of hospitals and the consequent lack of medical supplies for the victims of violence cannot be justified.
"We call upon those responsible for conducting the war to respect the lives of all civilians and to work unceasingly for a peace based on justice. War can never be a satisfactory solution to political problems."
Last week the leader of English and Welsh Catholics, Cardinal Vincent Nichols, told Premier the situation in the Middle East with millions being made refugees was the "crisis of our times".