The Most Rev Justin Welby said on social media on Tuesday that he was "personally very sorry for this terrible atrocity" after visiting the site of the Jallianwala Bagh massacre in the north-west Indian city of Amritsar.
More than 300 people were killed and 1,200 injured when troops under British command fired into a crowd of protesters in April 1919.
Mr Welby posted on Facebook that visiting the site had aroused a "sense of profound shame" at what had happened.
He added: "I feel a deep sense of grief having visited the site of the horrific Jallianwala Bagh Massacre today in Amritsar, where a great number of Sikhs, as well as Hindus, Muslims and Christians, were shot dead by British troops in 1919.
"I have no status to apologise on behalf of the UK, its government or its history.
"But I am personally very sorry for this terrible atrocity.
"It is one of a number of deep stains on British history.
"The pain and grief that has transcended the generations since must never be dismissed or denied."
In 2013 David Cameron became the first serving prime minister to visit the site of the 1919 massacre, bowing his head in honour of the hundreds of people killed.
Writing in a book of condolence, he said the episode was "deeply shameful" and should never be forgotten.
But he stopped short of apologising, saying that this would not be appropriate as the killings were condemned at the time by the UK authorities.
Earlier this year former prime minister Theresa May called the killings a "shameful scar" in British-Indian history, but stopped short of formally apologising.
Mr Welby said that the past must be learned from so that nothing like the Jallianwala Bagh Massacre ever happens again.
He added: "When there is something on the scale and horror of this massacre, and done so many years ago, words can be cheaply banded around, as if a simple apology would ever be enough.
"Learning of what happened, I recognise the sins of my British colonial history, the ideology that too often subjugated and dehumanised other races and cultures.
"Therefore, we have a great responsibility to not just lament this horrific massacre, but most importantly to learn from it in a way that changes our actions."
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