In a question presented by Stuart Exelby from Doncaster Unite, the union retired members branch, he asked Mayor Jones if the council would '˜give a commitment to continuous support' for all concessionary travel.
Mayor Jones said the issue for free bus travel in England was a national policy matter but rail travel for elderly and disabled people was made through the South Yorkshire Passenger Transport Executive (SYPTE).
She added there was '˜no plans' for this to change but would challenge any movement in policy if it arose in future.
Mr Exelby said: 'As long as Doncaster Council and its councillors take the Government on, if they show any response in taking the concessionary travel away from the people.
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'If you take the Tories on, you will get the full backing of Unite the union.'
Mayor Jones responded: 'This is a national scheme - therefore it cannot be changed unless the decision is made by central government. Only the discretionary concession of free rail travel for the disabled and half-price rail fares within South Yorkshire for the elderly is a decision that can be changed at local level.
'We are not aware of any plans to remove this at this time. We recognise the benefits not just to the economy of this scheme but also to the health and well being of our residents.
'If we become aware to any threat to the scheme then we will challenge this.'