Most Revd Justin Welby gave a speech at the at the city's Church of Our Lady or Frauenkirche during a service attended by the President of Germany, Joachim Gauck, and German church leaders.
Archbishop Justin said: "Walking together as friends requires talking together in truth. As Croatian theologian Miroslav Volf challenges us: 'To remember wrongdoing untruthfully is to act unjustly.'
"Much debate surrounds this most controversial raid of the allied bombing campaign. Whatever the arguments, events here seventy years ago left a deep wound and diminished all our humanity.
"So as a follower of Jesus I stand here among you with a profound feeling of regret and deep sorrow."
An estimated 25 thousand people died in the British and American attack, which created a firestorm that left the city in ruins.
The city was believed by Allied forces to be a vital Nazi command centre.
