It also neither ‘supports nor opposes’ the activity.
The organisation also believes ‘it can have positive and negative environmental impacts’. But on the land it owns, ‘sporting shooting’ has not been permitted since 1981.
The PDNPA responded after two hen harriers disappeared and two nests with a total of 10 eggs were lost on National Trust land in the national park last month.
The incident prompted Dr Ruth Tingay, of Raptor Persecution UK, to call for a ban on driven grouse shooting across the entire national park.
She said: ‘That would seem to be a far more effective prospect than a piecemeal approach by the National Trust, at least in terms of tackling the rampant raptor persecution taking place'.
But a PDNPA spokeswoman said: “We have no powers to control shooting other than on land that we own (less than 5 five per cent of the Park), where sport shooting has not been permitted since the 1980s.”
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The reasons for the disappearances were unknown and South Yorkshire Police were investigating, she added.
In May, the PDNPA revealed successful nesting attempts for the hen harrier in the Peak District ‘remain firmly in single figures across almost two decades’.
In 2019, Natural England reported on a 10-year study which suggested there was ‘widespread illegal killing of hen harriers on English grouse moors’. It found the likelihood of hen harriers dying, or disappearing, was 10 times higher in areas predominantly covered by grouse moor, compared to areas without.
It also revealed that 72 per cent of tagged harriers were either confirmed or considered very likely to have been illegally killed.
Hen harriers are strictly protected under Schedule 1 of the Wildlife and Countryside Act 1981. It is an offence to intentionally or recklessly disturb them on or near an 'active' nest.
They are also on the Red List of UK birds of conservation concern.
Some 70 hen harriers have been confirmed ‘missing’ or illegally killed since 2018, most of them on, or close to, UK grouse moors, according to Dr Ruth Tingay.
South Yorkshire Police have been contacted for comment.