Edinburgh Western Lib Dem Alex Cole-Hamilton said access to a computer was even more vital during the pandemic yet many were missing out.
He is calling on the Scottish Government to increase funding for the city council so more cleaners can be employed to ensure libraries are able to reopen safely.
All the Capital’s libraries closed in March because of Covid. Six reopened in October and another four – Wester Hailes, Craigmillar, Gilmerton and Drumbrae – are due to open next month.
But any further reopenings are difficult because cleaners have had to be redeployed from libraries and other council buildings to increase the number in schools.
Mr Cole-Hamilton said: "Whether it is enquiries about council tax, registering a child for school or job hunting, access to a computer and the internet has become more essential because of the pandemic. Large areas of Edinburgh are digitally excluded if they don’t have a computer at home or a car to travel to a library that is open.
"Clearly the demand for cleaning is high and rightly so, but this demand will not be reducing any time soon and we need equality of access to our libraries now more than ever.
"We are going to have students returning home from university soon and some of them will also require access to the library for books as well as computers.”
He said extra government funding for councils to deal with Covid clearly was not enough to keep schools and libraries open. “These are both essential services, and councillors should not be having to choose which communities can benefit and which lose out.”
When Mr Cole-Hamilton raised the issue at Holyrood, Communities Secretary Aileen Campbell told him the government had produced guidance to help councils reopen libraries safely, but it was up to individual councils to decide when to reopen. But she agreed libraries provided “critical services” for people.
Edinburgh culture convener Donald Wilson said “The Council’s plans are for a phased and safe reopening of local facilities, including libraries, which play such a vital part in the health and wellbeing of our local communities.”