North Yorkshire Police today detailed how the men were caught on camera approaching the nest site on six occasions back in May.
The marsh harriers, which are a protected breed, had been discovered nesting on moorland forming part of Middleton and Denton moors earlier that month.
The site was being monitored by RSPB investigators, who photographed the nest containing five eggs and observed adult birds there.
But on May 17, a camera set up to record activity at the nest site caught at least two individuals, who appeared to be men, going near the nest six times between 12.40pm and 9.30pm.
The sound of several shots fired in the vicinity of the nest were recorded, as was the noise of an engine, believed to be a quad bike.
One of the men stood over the nest, bent down, and appeared to pick up something from the nest before walking away.
The pair wore dull, brownish green coloured jackets, traditional country caps, and carried what looked like shotguns and a brown game bag
The following day at around 9.40am, a further visit was made by a similarly dressed man who carried a green rucksack.
This individual stood over the nest, bent down, and appeared to remove something from the nest.
When an RSPB investigator checked the site on 19 May, they found the nest was empty and there and there was no sign of any debris from damaged eggs.
A number of men have been spoken to by police as part of the investigation, but the people shown on the video at the nest site have not been identified.
PC Bill Hickson, who is investigating the incident, said: “The video evidence provided by the RSPB shows illegal activity around a marsh harrier nest, and the activity shown speaks for itself.
"The pictures on the video are, unfortunately, too small to produce an image from which any of the individuals shown could be identified.”
The Wildlife and Countryside Act 1981 makes it an offence to take, damage, or destroy the nest of any wild bird.
Marsh harriers are a scarce species, listed on schedule 1 of the act, and have additional protection.
It is an offence to intentionally or recklessly disturb birds listed on schedule 1 while they are at, or near, a nest with eggs or young.
Anyone with information is asked to email [email protected] or call North Yorkshire Police on 101, choose option 2 and ask for PC 820 Bill Hickson.