The massacre took place on April 13, 1919, when British troops, commanded by Brigadier-General Reginald Dyer, opened fire at a crowd of unarmed people, on the harvest festival of Baisakhi.
The British Foreign Office said in a statement: "As the former Prime Minister said when he visited the Jallianwala Bagh in 2013, the massacre was a deeply shameful act in British history and one that we should never forget".
Khan, who was on a three-city tour of India, visiting Mumbai, New Delhi and Amritsar, later crossed over to Pakistan from the Attari-Wagah land border, about 30 km from here.
Several British politicians, including former Prime Minister David Cameron, had expressed regret over the massacre, but stopped short of apologising. "It is time for the British government to finally apologise", he wrote. Cameron defended his decision to not offer a formal apology by saying: "So I don't think the right thing is to reach back into history and to seek out things you can apologise for. This is about properly acknowledging what happened here and giving the people of Amritsar and India the closure they need through a formal apology", Khan said as he visited the Jallianwala Bagh memorial and paid respects.
Khan, who is from the Opposition Labour Party, does not speak for Britain's Conservative government.
Though British monarch Queen Elizabeth and her husband Prince Phillip visited the Jallianwala Bagh in October 1997, no apology for the massacre was offered. In two years, it will be 100 years since the massacre.
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In May, he took over the theatre command from Lucky Irabor who is now coordinating the Multinational Joint Task Force (MNJTF). Rogers Nicholas former Chief of Logistics at the Army Headquarters, Abuja has been appointed to replace him.
A British commission that conducted an inquiry into the incident concluded 379 people were killed but Indian leaders estimated up to 1,000 people had died in the firing.
Khan went around the Jallianwala Bagh complex and saw the Martyr's Well and the bullet marks on the walls.
The British monarchy and the United Kingdom government have so far not issued a formal apology over Jallianwala Bagh.
Earlier this morning in Amritsar, Sadiq Khan also visited Sri Harmandir Sahib, often known as The Golden Temple, which is the most important pilgrimage site of Sikhism.
Almost 100 years later, it remains a controversial subject as many British dignitaries, including Queen Elizabeth and her husband, Prince Phillip, and former prime minister David Cameron, have visited Jallianwala Bagh to pay their respects.
Today's visit forms part of the Mayor's six-day mission to India and Pakistan to strengthen their cultural and economic ties with London.
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