Conservationists have urged the Scottish government to regulate grouse moors after two golden eagles disappeared within hours of each other on a shooting estate in Perthshire.

The two juvenile eagles were fitted with satellite tags which abruptly stopped sending out signals on 18 April – the latest of a spate of cases where birds of prey have disappeared or been found dead in the same area of Perthshire, known as Strathbraan, near Dunkeld.

One of the eagles was tagged last year by Andy Wightman, a Scottish Green party MSP who is the golden eagle “species champion” in Scotland, as part of a bird of prey conservation project led by the broadcaster Chris Packham and Ruth Tingay, who blogs for Raptor Persecution UK.

Wightman had named the bird Adam after the revered Scottish mountain ecologist Adam Watson, who died in January this year.

Wightman, an expert on land reform, said the eagle’s disappearance had left him distraught and he had written to Nicola Sturgeon, Scotland’s first minister, asking her to outlaw intensive grouse shooting.

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“I was gutted; very, very angry,” he said. “This latest outrage should be a wake-up call to the Scottish government that for all their reviews, inquiries and reforms, rampant criminality remains in place across many of Scotland’s driven grouse moors.”

There are several areas of the Highlands with no breeding eagles present. These “open territories” attract large numbers of juvenile eagles looking for new territories, food and nesting sites, yet fail to colonise them. Scottish Natural Heritage, the government’s conservation agency, believes it highly likely they are also killed to protect grouse stocks on shooting estates.

Last week the Royal Society for the Protection of Birds revealed that the partially-decomposed body of a satellite-tagged hen harrier called Rannoch had been found on another estate in the Strathbraan area. The harrier had been caught in an illegal spring trap, which was still attached to its left leg.

The RSPB said it was the 23rd case where a bird of prey had allegedly being persecuted in Strathbraan since 2000. They have included poisoned red kites, trapped buzzards and other tagged hen harriers, and the golden eagles which disappeared in April.

The birds’ last satellite signals were recorded on the Auchnafree shooting estate near Dunkeld, at 6.25am and 11.39am respectively, several kilometres apart. Both birds were at ground level when their last signals were received, their tags showed.

The final six signals for Wightman’s tag show it just beside a vehicle turning circle at the end of a hill track on the grouse moor. The estate and the sites of the eagles’ last signals were searched by the police in late May but nothing suspicious was found, and no one was arrested or questioned. The birds were not found and the circumstances of their disappearance remain unknown.

In a statement, Auchnafree Sporting, the group which runs grouse shooting on the estate, said: “We see eagles frequently on the estate and have no problem with them. We assisted police with their investigation and wholeheartedly support the appeal for information.”

Alix Whitaker, a member of the family which owns Auchnafree, said they had asked neighbouring estates for help tracing the birds and urged anyone with information to contact the police. “We were absolutely shocked to learn that these two eagles were missing. They have been around the estate for some time now and we were delighted to have them,” she said.

Ian Thomson, RSPB Scotland’s head of investigations, said the latest cases added to the need for the Scottish government to licence grouse moors, to give ministers the powers to ban shooting estates where protected species are disappearing.

It is thought Roseanna Cunningham, the Scottish environment secretary, is minded to introduce licensing if a Scottish government review of grouse moors chaired by Prof Alan Werritty, which is due to submit its final report to her this month, agrees it can be done.

Thomson said: “The killing of birds of prey on land managed intensively for driven grouse shooting continues unabated, and indeed has intensified in some areas. We repeat our call on the Scottish government to take urgent action to regulate this industry that is clearly causing serious damage to significant aspects of our vital natural heritage.”

The RSPB and SNH believe golden eagles are particularly vulnerable in Strathbraan because no breeding pairs have been able to settle and breed successfully there. The RSPB alleges this is due to deliberate persecution.