He described it as "an extraordinary event, a monstrous event, an event which stands in singular and sinister isolation" and which was "not the British way of doing business".
The Punjab chief minister said he heard Khan's remarks on the Jallianwala incident and was happy to know about his feelings on the matter.
At the Jallianwala Bagh memorial and garden, the Mayor met with ancestors of those who escaped the massacre and laid a wreath at the foot of the memorial to pay his respects.
On April, 13, 1919 troops from the British Indian Army fired on unarmed civilians in India, killing hundreds and wounding many more.
Colonial-era records show about 400 people died when soldiers opened fire on men, women and children in the enclosed area, but Indian figures put the toll at closer to 1,000. The memorial was inaugurated in 1961 and serves as a way to remember those who died and were injured in the massacre.
He said it was time for the British to apologise for the Jallianwala Bagh massacre. "Some people used the word massacre", the Mayor said.
Light snow is on the way
Otherwise, expect partly cloudy skies, brisk breezes, and colder temperatures to be the rule through the rest of the weekend. As that front looks to be fairly far off the coast, most of the moisture should stay out over the ocean as well.
Sadiq Khan extended his apologies during today's visit but made it clear that a formal Government apology should have been given decades ago and that, ahead of the centenary of the massacre, it is more important now than ever that the Government properly acknowledges what happened at Jallianwala Bagh to ensure something like this can never happen again.
Khan, later on Wednesday, visited the Golden Temple complex, where the holiest of Sikh shrines, Harmandir Sahib, is located and offered prayers.
Mr Khan also visited the Langar hall, the largest community kitchen in the world, of the shrine complex and partook langar while sitting on the floor.
Mr Khan was also presented with a Siropa (robe of honour) by the officials of the Shiromani Gurdwara Parbandhak Committee (SGPC).
Former Prime Minister David Cameron had visited Amritsar, home to the famous Sikh Golden Temple, at the end of a trade mission back iASn 2013.
Mr Khan, who was on a three-city tour of India, visiting Mumbai, New Delhi and Amritsar, later crossed over into Pakistan from the Attari-Wagah joint check post land border between India and Pakistan, about 30 km from Amritsar.