Farmers have been calling for a cull of the species as the birds attack livestock.
Angus McNeil, a former MP for the Western Isles, said in 2022 that two of his neighbour’s healthy four-day-old lambs had been “ripped apart” by eagles and posted gruesome videos of them online.
NatureScot said it had been contacted about missing Shetland pony foals and that they may have been “predated by sea eagles”.
Cameron told the Sunday Post he hoped an investigation of the birds’ nests and feeding remains would confirm his suspicions and allow action to be taken.
“I can’t see any other explanation,” he said.
He said the birds – which can have a wingspan of up to 8ft – arrived on the island about eight years ago.
“They’re not dissolving into thin air,” he said of his foals.
“We have had Shetland ponies for 60 years-plus, and nothing like this has happened before.
“The only difference in the last few years is that we have a bigger presence of white-tailed eagles.”
A NatureScot spokesman told The Daily Telegraph: “While there is currently no direct evidence to support this view, we will be analysing prey remains from sea eagle nests across North and South Uist this year to help inform our wider work with farmers and crofters on the issue of predation.
“This will include visits to nest sites near the person’s holding.
“We provided advice on issues of lamb predation reported by this individual at a site visit in 2023, including a wide range of support options available through the Sea Eagle Management Scheme.
“Some of these options may be helpful in protecting both sheep and ponies.”
Farmers have since been further angered by plans to reintroduce golden eagles into England after they were successfully returned to southern Scotland from the Highlands.
Abi Reader, the deputy president of NFU Wales, told the BBC they “represent a threat to livestock farmers ... particularly [for] those who are farming sheep”.
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