Colombian rebels holding a British man and four Israelis say they plan to release their hostages before the end of the year.
There are renewed hopes Mark Henderson could be home for Christmas
The National Liberation Army (ELN) statement came a week after the group said it would not release Mark Henderson and his fellow captives because of military operations in the Sierra Nevada mountain region.
But rebels say their change of stance has arisen from concerns the hostages could be accidentally killed by the Colombian military.
Mr Henderson's father, Christopher, said the family was on an "emotional rollercoaster" over the recent hopes and disappointments.
He said: "We've used the expression quite a lot, but it's been an emotional rollercoaster.
"I think we've learned now not to pin all our hopes so, you know, this could still fall through and we could be in the New Year before they are released."
But the Foreign Office has welcomed the news, which raises hopes that Mr Henderson, originally from Lincoln, could be home with his family in North Yorkshire before Christmas.
The ELN said: "As proof of our flexibility and maturity, we promise to liberate the hostages in the upcoming days, hopefully before the end of the year, to avoid such a tragedy."
Monsignor Hector Fabio Henao, a Catholic Church mediator, said: "We maintain hope that this can be done very quickly.
"We are aspiring for Christmas time."
A Foreign Office spokeswoman said: "We welcome the statement from the ELN and look forward to the release of Mark Henderson in the near future."
The 32-year-old television producer's family, who live in Pateley Bridge, North Yorkshire, recently spoke of their disappointment after hopes of his release before Christmas were dashed.
Speaking on 9 December, his mother Sharelle said: "The church has worked non-stop to make sure something happens and, while we are disappointed at this stage, hopefully the situation will change again and he will be home for Christmas.
The hostages were kidnapped in the Sierra Nevada mountains
"It's all hope anyway until he is on that plane and hopefully it could all change again."
Mr Henderson was seized with seven other backpackers in the Sierra Nevada Mountains on 12 September.
A second Briton, Matthew Scott, 19, from Clapham, south London, made a daring escape two days later.
A German and a Spaniard were freed by the rebels at the end of November.