The authority said talks with town and parish councils about taking over such assets to prevent them from closing had been "encouraging" and would continue over the next few months.
It comes after officials at Church Stretton Town Council and Ludlow Town Council requested more time to manage the transfer of services. The services will need to be funded or managed by town councils or third party organisations from April 2017 as Shropshire Council plans to cut its leisure and culture budget to zero as part of cost-saving measures.
Venues under threat in the two towns include Ludlow Library and Museum Resource Centre, Church Stretton Library, South Shropshire Leisure Centre and Teme Church Stretton Leisure Centre.
Ludlow Town Council said it would need an extra year – until April 2018 – to properly work out and consult on such a large transfer.
Councillor Michael Walker, mayor of Church Stretton, wrote to Malcolm Pate, leader of Shropshire Council, saying time allowed was "unrealistic" and "way beyond the capacity" of either town council or Shropshire Council staff.
George Candler, Shropshire Council's director of commissioning, said talks were ongoing and would be kept continually "under review".
He said: "Shropshire Council has been encouraged by the discussions that have taken place thus far in relation to those service areas that are at risk from April 2017 onwards.
"We recognise the timescales are challenging, which is why we alerted town and parish councils to this at a meeting back in January 2016.
"Since then officers have been working hard with town and parish councils, as well as the voluntary and business sector, to see how we can ensure the long term sustainability of these important community facilities."
Councillor Walker said he was sceptical that Shropshire Council will be in a position to either transfer funding responsibility or decommission services in April next year.