The trustees claim they are being "targeted personally and intimidated" over the appointment of Professor Alexander Stoddart to design a statue of Elsie Inglis.
He was unveiled after an official competition to find an artist to honour the trailblazing surgeon, physician and suffragist was suspended days after the Queen’s funeral.
A new statement has been issued by the trustees after they announced they would not be dropping the royal sculptor from the project or re-running the statue contest, despite issuing an official apology over the handling of his appointment.
When the campaign was put on hold last month, the charity’s trustees raised concerns about the “level of vitriol” they had experienced, describing some of it as “bordering on the defamatory”.
The Statue for Elsie Inglis charity has repeatedly refused to name its five trustees amid criticism over a lack of transparency. An open letter posted on its official Facebook page suggested decisions were made “behind closed doors and without public consultation or scrutiny”.
However, the campaign says trustees have been targeted personally after their identities were "uncovered".
Former Lord Provost Frank Ross launched a competition to find an artist in July for “an enduring and immutable memorial to one of Scotland’s greatest women”.
However, the Statue for Elsie Inglis Trust has admitted approaching Prof Stoddart after the death of the Queen, saying the rethink was prompted by scenes of her coffin being carried along the Royal Mile.
The new statement from the charity said: “We are being pressed to release the trustees’ names and fully accept that in ordinary circumstances we have a legal duty to provide this information upon request.
"We want to be transparent. However, with the greatest reluctance we have decided not to share their names at this time because we have concerns about their safety.
"This is not a decision that we have taken lightly. Trustees whose names have been uncovered are now being targeted personally and intimidated.
“We have reported this to [charity regulator] OSCR and have also referred to its guidance, which states that trustees can withhold this information where doing otherwise is likely to jeopardise their own safety or security.
"We have apologised to those impacted by our change of process when commissioning the statue and are now focused on delivering what will be a fitting monument to Elsie Inglis.”
Edinburgh-born Prof Stoddart, the creator of the statues of David Hume and Adam Smith on the Royal Mile, is the King’s Sculptor in Ordinary in Scotland.
When his appointment was announced, Prof Stoddart said he was “very pleased and honoured to be asked to undertake this important task”.
But he has been accused of downplaying the significance of Inglis becoming the first woman to be commemorated on the Royal Mile, by stressing the importance of preserving “the seriousness of the High Street as a place of immense historical import”.
However, the charity has suggested that some critics of his appointment seem more interested in “promoting women’s rights” rather than honouring Inglis.