The Colombian government revealed on Thursday that Luis Manuel's captors were militant insurgency group the National Liberation Army (ELN).
Later in the day a representative of the ELN gave a statement claiming that the release of Diaz's father was imminent.
In the video clip, ELN member Juan Carlos Cuellar said that Luis Manuel would be released "as soon as possible", in what is a significant development in the case.
The ELN was founded in 1964 and remains one of Colombia's most powerful insurgent groups.
They entered into a ceasefire with the Colombian government back in August in an attempt to forge peace. Interior minister Luis Fernando Velasco claimed on Thursday that this ceasefire had been violated with the kidnapping, prompting the ELN's video response.
Diaz's father was taken on Sunday alongside his mother, Cilenis Marulanda, by armed men on motorbikes. Marulanda was released after a few hours but Luis Manuel has been missing ever since, with fears he may have been smuggled over the border to Venezuela.
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