Prime Minister David Cameron is facing calls to apologise and pay financial reparation for Britain's role in the historic slave trade in the Caribbean.
The demands from campaigners have threatened to overshadow the PM's visit to the island, where he was announcing £25m in British aid for a new Jamaican prison.
The country's PM Portia Simpson-Miller said she had raised the issue in talks.
Mr Cameron ruled out paying reparation, saying it was "not the right approach".
He said his visit - the first by a British prime minister in 14 years - was to "reinvigorate" ties between the countries, and he wanted to concentrate on future relations not centuries-old issues.
Ms Simpson-Miller said while she was "aware of the obvious sensitivities", Jamaica was "involved in a process under the auspices of the Caribbean Community to engage the UK on the matter".
For more than 200 years Britain was at the heart of a lucrative transatlantic trade in millions of enslaved Africans.
According to ship records it is estimated about 12.5 million people were transported as slaves from Africa to the Americas and the Caribbean - to work in often brutal conditions on plantations - from the 16th century until the trade was banned in 1807.
In 1833, Britain emancipated its enslaved people and raised the equivalent of £17bn in compensation money to be paid to 46,000 of Britain's slave-owners for "loss of human property". University College London has compiled a database of those compensated.
Among those listed is General Sir James Duff, who it is claimed is a first cousin six times removed of David Cameron. He was awarded compensation worth around £3 million in today's terms.
Others who received compensation include the ancestors of novelists George Orwell and Graham Greene, and distant relatives of Arts Council chairman Sir Peter Bazalgette, and celebrity chef Ainsley Harriott.
The issue of slave-owning nations compensating former colonies is a contentious one in the Caribbean, where national commissions have calculated the sums could run into trillions of dollars.
One suggestion has been that the money could be provided in the form of debt relief.
Mrs Simpson Miller told the United Nations in 2013 there should be "an international discussion in a non-confrontational manner" and its parliament had passed a motion backing reparations.
One Jamaican MP, Mike Henry, threatened to boycott Mr Cameron's speech at the country's parliament later if he does not engage on the issue.
"If it is not on the agenda, I will not attend any functions involving the visiting prime minister, and I will cry shame on those who do, considering that there was not a dissenting voice in the debate in parliament," he told The Gleaner newspaper.
Campaigners also called on Mr Cameron to make a personal apology, saying one of his own ancestors was paid compensation for the loss of his slaves in 1834.
Records suggest General Sir James Duff was a first cousin six times removed of the PM, and was awarded compensation worth around £3 million in today's terms.
Bert Samuels, a member of Jamaica's National Commission on Reparations, told Television Jamaica "he needs to atone, to apologise personally and on behalf of his country".
Sir Hilary Beckles, who chairs Caricom's Reparations Commission - which represents Caribbean nations - wrote in an open letter in the Jamaica Observerthat the UK must "play its part in cleaning up this monumental mess of Empire".
He said Mr Cameron was "a grandson of the Jamaican soil who has been privileged and enriched by your forebears' sins of the enslavement of our ancestors".
Mr Cameron made no mention of the issue after Wednesday's talks - but Number 10 said he had made clear to his opposite number that he "understood it was an issue for some people".
He reiterated the "long-standing position of the United Kingdom that we do not believe reparations is the right approach".
Speaking to reporters on the flight to the Caribbean, Mr Cameron made clear he did not want to focus on the issue.
"This is about the future relationship and about what we should be doing together economically in terms of trade and investment and this significant infrastructure fund I am announcing," he said.
Labour leader Jeremy Corbyn, who lived in Jamaica for two years in his youth, said that, as prime minister, he would be ready to apologise for the slave trade.
Speaking at Labour's annual conference in Brighton, Mr Corbyn said it was "the most brutal part of our history and the history of Jamaica".
On his two-day visit, Mr Cameron announced a £300 million development package for the Caribbean, to provide grants for infrastructure projects including roads and bridges.
He also revealed that the UK will spend £25m on building a prison in Jamaica so that foreign criminals in the UK can be sent home to serve sentences in the Caribbean.
More than 600 Jamaican nationals are in UK jails but cannot be deported because of Jamaica's poor prison conditions.
Officials say the foreign aid-funded deal could save taxpayers £10m a year when transfers begin in 2020.
The Howard League for Penal Reform criticised the plan, saying it was "the wrong use of foreign aid", and would fail to address the real issue of overcrowding in British prisons.