Most Revd Justin Welby also pointed to Jesus Christ, who did not resort to violence but instead sacrificed his life for people who wanted to kill him.
He's speaking after 38 people were killed after a gunman opened fire on a beach in the Tunisian holiday resort of Sousse. The man hid the gun in a beach umbrella before murdering the tourists. Islamic State claimed responsibility for the attack.
At least eight of those killed are Britons, with the Tunisian Prime Minister Hassib Essid confirming most of the victims were from the UK.
The massacre has prompted thousands of holidaymakers to return home early on special flights.
On the same day, extremists attacked a gas factory in the French city of Lyon. They drove a car into the factory causing an explosion which injured two people. A man was also found beheaded.
A 35-year-old father of three, Yassin Salhi, is being questioned by police. The attack prompted the French Prime Minister, Manuel Valls, to say that "the question is not if there will be another attack, but when."
And in Kuwait, Islamic State also claimed responsibility for a bombing on a Shia mosque which killed 27 people and injured 200 more. It is Kuwait's worst extremist attack in decades. Kuwaiti authorities say they have made "numerous arrests in connection" with the attack.
All three acts of terrorism took place within three hours of each other.
Most Revd Welby said: "All of us must be full of grief at the attacks in Tunisia, France and Kuwait. They are intended not only to destroy but to divide, not only to terrify but to take from us our own commitment to each other in our societies.
"Let us together mourn for the victims, weep with the bereaved, support the injured and pray for them all to the God who in Jesus Christ went to the Cross and died rather than bearing a sword.
"Facing such a global and long term menace, we are called to reaffirm our solidarity with each other and affirm the great treasures of freedom, in religion and so many other ways.
"Our strength is in the God who conquered evil when Jesus rose from the dead, and on His death and victory we find the basis for our future."