Figures show Glasgow City Council operates 112 nurseries across the city, but only 39 offer extended hours between 8am and 6pm.
The figures also show the authority's nurseries offer a total of 13,883 places across the city, but only 23 per cent of these - some 3183 - cover the working day.
Parents highlighted the figures in a continuing row over how the council is delivering the Scottish Government's promise to offer families a mandatory 600 hours of funded early learning and childcare for three and four-year-olds.
Councils are expected to use part of their overall block grant to provide enough free places for parents in their area.
Glasgow does this by funding places in its own nurseries first and then paying partnership providers in the private sector for the additional demand.
However, a survey by campaigning parents has already shown hundreds of Glasgow children are unable to secure fully funded places at the private nurseries they currently attend.
The council argues there are enough places available in state-run nurseries to meet demand, but campaigners say the new figures prove the places are not suitable for working families because they cover only part of the day.
Jennifer Gorevan, a spokeswoman for the campaign to secure free places for all parents, said: "In Glasgow there are hundreds of children in partnership nurseries who are eligible for early years funding, but cannot access their entitlement.
"Meanwhile, there are thousands of council nursery places sitting empty because the half-day, term-time only model of provision that they offer is extremely difficult, if not impossible for working parents to take up.
"Someone must take responsibility for ensuring the Government's promise of free childcare for all becomes a reality. The current system is not fit for purpose and working families are losing out."
Shirley Hexley, the owner of Clarence House Nursery, Maryhill, said: "The council needs to address the problems working parents are facing when trying to access their child's free educational hours.
"This is an entitlement all three and four-year-olds have been promised by the Scottish Government, and it is just not being delivered."
However, a spokeswoman for the council said there were more than enough places for eligible parents in Glasgow.
She said: "We have nearly 14,000 nursery places that meets our duty to provide up to 600 hours for every three and four-year-old in Glasgow. This is over 1,000 more than required.
"We do try to support working families through extended day and full-time places, but it is just not possible for us to meet the needs of every family that needs full-time childcare."
The row has prompted calls for the Scottish Government to change the policy to ensure parents get funding wherever they send their children.
Purnima Tanuku, chief executive of the National Day Nurseries Association Scotland, said recently that the current system was greatly restricting the choice of parents and called for funding to follow children.
The Scottish Government said every council had a legislative duty to consult parents about where free places should be allocated.
The issue has also impacted on parents in East Lothian, where the council has capped the number of places it funds in private nurseries.