Job losses are "inevitable" as the authority looks to make another £30 million worth of savings over the next two years.
Telford & Wrekin Council finance chief Councillor Lee Carter said the authority had no choice but to slash front-line services after already making £80 million worth of cuts and axing more than 1,000 jobs since 2010.
He blamed Chancellor George Osborne for further cuts to the amount of cash the council gets in the form of a yearly grant from government.
The council will get 20 per cent less next year compared to 2015/16.
Libraries in Dawley, Donnington, Hadley, Madeley, Newport and Stirchley face the axe.
Markets in Madeley, Hadley, Dawley, Ironbridge, Oakengates and Newport will shut.
See below: The key areas of council services that will be affected by the cuts
An urgent review of the management of the five council-run community centres has begun and youth clubs and children's centres will also be hit.
Councillor Carter said consultation would now start with parish and town councils and other interest groups to see if there were ways of keeping the under-threat services running. But if no arrangements can be made, the most contentious cuts will come into force from April next year.
The finance chief said: "It's an extremely difficult budget, possibly one of the most difficult the authority has ever had to put together.
"It's not something as an administration that we would have ever wanted to consider. None of us came into politics to make these kinds of cuts.
"Unfortunately we have been dealt a really horrible hand by the Chancellor. What I would say from evidence is that fairness and compassion has to be at the heart of what we do.
"This has almost been a last resort for us – we have worked so hard over the past four years to protect front-line services, services that matter most to the community.
"We have put the most contentious of the cuts into year two to give us the time to go out and work with people to find a way of keeping these services running. We will always care for the must vulnerable in our community, the elderly and the young."
On the possibility of job losses, Councillor Carter added: "I think it's folly to put a number on it.
"It's inevitable there will be some redundancies but I would urge people to look at our track record so far. Out of the 600-odd redundancies we have made in the last few years, only 64 were compulsory. That demonstrates our approach."
A consultation on the plans starts this week and runs until February 7. Further information is available at www.telford.gov.uk/budget
It was also revealed today that council tax could be hiked by nearly four per cent in Telford from April.
The key areas of council services that will be affected by the cuts:
Proposals include the closure of council-run libraries in Madeley, Stirchley, Donnington, Dawley, Newport and Hadley.
Libraries at Southwater, Wellington and Oakengates will remain open. Council chiefs say the move, which also includes axing the mobile library service, will save a total of more than £530,000 per year in staff and costs.
The council is carrying out an urgent review of the management of five community centres it runs in the borough.
They are Brookside Community Centre, Leegomery Community Centre, Donnington Wood Lifelong Learning Centre, Sutton Hill Community Centre and Watling Street Community Centre in Arleston.
Savings have not yet been identified.
The council is developing a new policy for school transport.
Council bosses admit it will have a significant impact on some pupils in the borough.
The proposed changes will generate a saving of £400,000 over the next two years, the report says.
The papers say it will impact on specific communities, particularly those in rural areas.
The council is proposing to shut 14 play areas bosses say are run-down or not well-used.
The move will save £28,000 per year, according to todays report.
They include Leegomery ball court and parks in Brands Farm Way, Randlay; Wrekin Avenue and Gravelly Drive in Newport; and Smallwood, Sutton Hill
Council bosses have earmarked the closure of a number of youth clubs run by the authoritys part-time youth workers.
No clubs have been named in the proposals, which are said to be worth a £300,000 saving to the councils annual budget.
Chiefs say they will look to support communities in setting up their own clubs.
The authority is proposing to axe council-run markets in Madeley (every Tuesday and Saturday), Hadley (every Wednesday), Dawley (every Friday), Ironbridge (first Sunday of month from May to Oct), Oakengates (every Saturday) and Newport (third Thursday of every month from Aug to Dec).
It will save the council £20,000 per year.