Mr Finlayson had replied to a letter from the former staff members by stating the museum was governed by a trust board, and he had no statutory responsibility for its administration, funding or appointment of board members, a ministerial spokesman said.
It is understood the staff group is supported by about 50 former museum staff members.
A member of the group said the continued loss of senior professional staff raised concerns about the long-term care of the collections.
Peter Entwisle, a Dunedin freelance journalist and fine arts curator, said yesterday he shared those concerns.
Specialised skills were required to support the core business of museums, which involved collecting, caring for collection items and communicating about them, both to the general public and to experts, Mr Entwisle said.
Otago Museum acting director, collections and research, Clare Wilson yesterday rejected the criticisms and said the museum had the required expertise to safeguard its collections and was well placed for a positive future.
The museum had decided to no longer employ one overall conservator, but to bring in specialised contract staff to help with the conservation of specific parts of the collections as required.
Labour arts and culture spokeswoman Steve Chadwick was also sent a copy of the group's letter, which she had drawn to the attention of Dunedin MPs Pete Hodgson and Clare Curran, party officials said.
Mr Finlayson had written to Otago Museum Trust Board chairwoman Margaret Collins, saying he had received letters and copies of media articles noting concerns raised by former museum staffers.
It was clear the correspondents had "negative perceptions of their previous employment conditions", but the place for them to address these, if they were valid, was through the Employment Relations Authority, he wrote.
"I understand high standards of care at the museum were acknowledged in the 2006 report by the Controller and Auditor-general on "management of heritage collections in local museums and art galleries".
It had been the Government's understanding that since working with the museum on its redevelopment project in the 1990s, storage standards and collection care and management had been substantially improved.
The Government had a "genuine interest in seeing the museum's important collections were properly cared for" and he would be interested in discussing this further with Mrs Collins, he said.
