Councillor Euan Jardine called on Live Borders, which operates the facilities, to make the step of reassessing its decision to keep libraries closed.
He said: “As the portfolio holder for culture it is becoming increasingly worrying that one of our main cultural assets has yet to open.
"Live Borders has done a fantastic job during the pandemic assisting with the Covid recovery and continues to do so. I understand that they still have staff on furlough and others working in vaccination centres. However, it is important that we start to get some services back to normal so that the community can continue to recover post pandemic.”
“I know that Live Borders restarted their mobile library service at the end of May, which is to be commended, along with the connect and collect service. But to myself and others, a library is more than just a place to rent books. It is a place to access computers or study.
"I have also been approached by people looking to print off applications for jobs but not sure where do do this. I offered to do it for them on my personal printer, but it should have been an easy visit to the library for this task.
"Libraries are also a focal point for tourists when they visit a town and for many they are a vital hub in the community.”
However, a spokesman for Live Borders said the time wasn’t right, as its staff were helping out with the vaccination and Test and Protect programmes.
He added: “Connect & Collect – where library books can be ordered online and collected from the mobile library – and the comprehensive eLibrary catalogue continue to be available.
“Galashiels Library reopened for an eight-week period from August 2020, but demand for its services was extremely low, although there continued to be high levels of usage of alternative library services.
“We have been clear that where achievable and sustainable the reopening of services may be accelerated and we continue to review the timeline on a weekly basis to consider what opportunities may arise and will keep customers updated.”