Home Secretary Sajid Javid told US Attorney General Jeff Sessions that the UK would not demand a “death penalty assurance” in this particular case.
He also indicated that he believed there was more chance of a successful trial in the US than in UK courts.
Alexanda Kotey and El Shafee Elsheikh, are said to have been members of the brutal four-man Beatles cell of IS executioners in Syria and Iraq, responsible for killing a series of high-profile Western captives.
The pair, who are understood to have been stripped of their British citizenship, were captured in January, sparking a row over whether they should be returned to the UK for trial or face justice in another jurisdiction.
In the leaked letter, obtained by the Daily Telegraph, Mr Javid said the UK “does not currently intend to request, nor actively encourage”, the transfer of Kotey and Elsheikh to Britain.
Promising support for the US, Mr Javid said Scotland Yard’s counter-terrorism command had been “engaged extensively” on the case with the FBI, with the investigation running for more than four years “during which time they have engaged with 14 other countries and compiled over 600 witness statements”.
Signalling that the UK was prepared to drop assurances relating to the death penalty, Mr Javid said: “All assistance and material will be provided on the condition that it may only be used for the purpose sought in that request, namely a federal criminal investigation or prosecution.
“Furthermore, I am of the view that there are strong reasons for not requiring a death penalty assurance in this specific case, so no such assurances will be sought.”
But he added: “As you are aware, it is the long-held position of the UK to seek death penalty assurances, and our decision in this case does not reflect a change in our policy on assistance in US death penalty cases generally, nor the UK Government’s stance on the global abolition of the death penalty.”
Mr Javid also said US courts were better placed to handle “foreign fighter” cases because of the risk of legal challenge in the UK.
The Home Secretary said he understood US “frustration” on the subject and added that the UK was introducing “new legislation to improve the range of offences on the statute book” to deal with the “scourge” of foreign fighters.
“Ensuring foreign fighters face justice raises a real challenge for all our jurisdictions; however, in this instance, we believe that a successful federal prosecution in the US is more likely to be possible because of differences in your statute book and the restrictions on challenges to the route by which defendants appear in US courts,” he said.
“The US currently has additional charges for terrorism offences which are not available under UK criminal law, and those offences carry long sentences.”
The Telegraph reported that other documents say that British officials have also assessed that the pair may be sent to Guantanamo without trial and that such an outcome will not be formally opposed.
Along with Mohammed Emwazi - the killer nicknamed Jihadi John - and Aine Davis, Kotey and Elsheikh are thought to have been part of a group named after the ‘60s band because of their English accents.
Emwazi, who was killed in a US air strike in 2015, appeared in a number of videos in which captives, including British aid workers David Haines and Alan Henning and US journalists James Foley and Steven Sotloff, were killed.
Davis was convicted of being a member of a terrorist organisation and jailed for seven-and-a-half years at a court in Silivri, Turkey, in May 2017.
Mr Foley’s mother, Diane, said she was opposed to the death penalty.
“I am very against that. I think that would just make them martyrs in their twisted ideology,” she told BBC Radio 4’s Today programme.
“I would like them held accountable by being sent to prison for the rest of their lives.”
The Home Office refused to comment on the leaked document.
But a spokesman said: “”We continue to engage with the US Government on this issue, as we do on a range of national security issues and in the context of our joint determination to tackle international terrorism and combat violent extremism.
“The UK Government’s position on Guantanamo Bay is that the detention facility should close.”