Petitioners want cuts to staffing levels and opening hours to be reversed.
They are also calling for the library to remain in its current location at Ionad Teampaill Chróine.
Councillors in the Glenties Municipal District were presented with a copy of the petition at their inaugural meeting in Dungloe this week.
The petition has also been sent to Eileen Burgess, County Librarian and to Seamus Neely, County Manager at Donegal Co Council, and Michael O’hEanaigh, Director of Community, Culture and Planning at Donegal County Council.
A spokesman said people in The Rosses are upset about the recent cut to the library’s opening times and the threat to move the library from its current location in Ionad Teampaill Chróine to the Public Services Building in Dungloe.
“The recent decision to close the library on Saturdays has been a major blow to Dungloe. Many people from the surrounding areas came to Dungloe to shop on Saturdays, and to use the library. Without the library they may choose to shop elsewhere, with access to a library.
“The one late night opening was very useful to many people who are at work or college during the day. Students in the area who have just completed their junior and leaving certificates hugely missed the lack of a library facility on any evening and on Saturdays in Dungloe,” said the spokesman.
Since the departure of one member of staff in April, the library must now close when the current sole staff member is not there – at lunchtimes but also during annual or sick leave.
“A town library having to close because of staff leave is not acceptable,” added the spokesman.
The library is an anchor tenant in the Ionad Teampall Chroine building and a move to the Public Services Building in Dungloe would have a negative impact on Dungloe – a town which is struggling to survive.
The Ionad hosts various functions that are enhanced by the library’s presence in the building, for eg, the annual cultural and literary Peadar O’Donnell weekend. The Ionad is a focus for arts and heritage and an integral part of the town.
The building, which was the old chapel in Dungloe, was renovated some years ago at a considerable cost and community effort and houses the library, a café, tourist information desk as well as a centre which runs classes and hosts arts events.
“The people of the Rosses are calling on Donegal County Council to employ another member of staff to enable the library to continue to serve the public well and for the well being of the town.
“The county council need to push for an exemption to the recruitment embargo for libraries in the county. We can’t be without a library service just because staff retire or leave,” added the spokesman.