David Cameron has laid a wreath at the memorial to the 1919 Amritsar massacre in India, describing it as "a deeply shameful event in British history".
The Prime Minister is using the final day of his visit to India to highlight the cultural ties that bind India and the UK.
He travelled to Amritsar, where he paid a visit to the Sikh Golden Temple, as well as the location of the massacre of Indian civilians by British troops.
He is the first serving Prime Minister to visit the Sikh holy city, the scene of one of the darkest episodes of the British Raj when hundreds died after British troops opened fire on a protest.
In the condolence book, Mr Cameron wrote: "This was a deeply shameful event in British history, one that Winston Churchill rightly described at the time as 'monstrous'.
"We must never forget what happened here, and in remembering we must ensure that the United Kingdom stands up for the right of peaceful protest around the world."
He wrote in the book in front of a plaque reading: "This place is saturated with the blood of those Indian patriots who were martyred in a non-violent struggle to free India from British domination."
An inquiry commissioned by the Raj colonial authorities found that 379 people died in the public gardens of Jallianwala Bagh, although Indian sources claim the death toll was 1,000 or more.
The atrocity - portrayed in Richard Attenborough's film Gandhi - was seen as an important turning point on the road to the end of British rule in India.
Descendants of some of those involved in the massacre showed Mr Cameron around, pointing out bullet holes in the wall and the Martyrs' Well where many died after seeking shelter from the bullets.
Asked why he had stopped short of apologising, the Prime Minister said: "I don't think the right thing is to reach back into history and to seek out things that we should apologise for.
"I think the right thing to do is to acknowledge what happened, to recall what happened, to show respect and understanding for what happened.
The memorial's secretary Sukumar Mukherjee, whose grandfather survived the shootings, said: "He has come here, he has paid his tribute here. It is more than an apology."
But Sunil Kapoor, 36, whose great-grandfather was killed, complained: "I'm not satisfied because he didn't meet the descendants. If you feel shameful, then why not make an apology?"
Mr Cameron's visit to the Punjab region - from where many British citizens originally hail - had a particular emphasis on the contribution of the 800,000 Sikhs living in the UK.
The Golden Temple is the most sacred site for Sikhs, whose religion requires them to spend one week of their lives volunteering to work within the Temple itself.
Mr Cameron donned a blue bandana to cover his head and removed his shoes and socks to tour the temple.
He also visited the kitchens, which feed thousands of pilgrims every day, where he tried his hand at flipping chapattis.
After the visit, he said: "In coming here to Amritsar, we should celebrate the immense contribution that people from the Punjab play in Britain, the role they play, what they give to our country.
"What they contribute to our country is outstanding and it is important to understand that and pay respect to that and to seek a greater understanding of the Sikh religion and that is why this visit to the holy temple, the Golden Temple, was so important."