Mr Pritchard spoke this week over plans that would hit Donnington, Hadley and Newport.
He said in the House of Commons: "Is the Leader of the House aware of the heartless cuts to local library services by Labour-led Telford & Wrekin Council, and may we have a debate on the vital role that library services play in communities such as Donnington, Hadley and Newport in my constituency?"
At the start of the year it was revealed that libraries, markets and community centres face the chop as Telford & Wrekin Council plans to make £30 million of cuts.
Meanwhile, Shropshire Council has said where libraries must be taken over by community groups or face closure under plans to save £1.1million from itsthe authority's £2.9million libraries budget.
The council said that job losses were "inevitable" and that the savings would be made over the next two years.
It has already made £80 million worth of cuts and axed more than 1,000 jobs since 2010.
But now, libraries in Dawley, Donnington, Hadley, Madeley, Newport and Stirchley face being closed along with markets in Madeley, Hadley, Dawley, Ironbridge, Oakengates and Newport.
Chris Grayling, Leader of the House of Commons, responded: "My honourable friend makes an important point. Library services remain of enormous importance to people in this country.
"It is striking how Conservative councils have faced the financial challenges, which all local authorities face, innovatively while still managing to deliver quality services, while Labour councils, all too often, cannot provide the efficiencies we need while protecting those services."
The call for a debate comes just days after Mr Pritchard said Newport has been "discriminated against" in the council's 2016 budget plans and vowed to help fight to save it from the axe.
He has held an emergency meeting with bosses at the borough council and said he "stands firm in the fight for library services".
This week the MP also launched an online petition against the cuts in a bid to save libraries in Newport, Hadley and Donnington.
He said they were "highly valued by the local community" and used by residents and community groups and said he would not work towards a "slash and burn" approach to cuts.
He said: "I will fight any plans to close any of these vital community assets. I hope local residents will join me in my campaign and sign my online petition."
To view Mr Pritchard's petition, visit www.surveymonkey.co.uk/r/wrekinlibraries