Wakefield's two main political parties have clashed over the issue of free TV licences for the over 75s.
The BBC said last week it was unable to fund the benefit except for those on pension credit, after the costs of free licences were passed onto them by the government.
Wakefield Council's ruling Labour party accused the government of "passing responsibility onto the BBC", but the Conservatives opposition leader branded the concept of TV licences an outdated "tax".
In its announcement last week, the BBC said that maintaining the benefit for those on pension credit only was "the fairest and best outcome".
Around 3.7million pensioners will be affected by the decision.
Speaking at a full council meeting on Wednesday, Wakefield Council leader Peter Box blamed the Conservatives for breaking their 2017 election manifesto pledge on the issue.
Theresa May had said a re-elected Tory government would pay for the licences, but this policy was later reversed.
Coun Box said: "What the government did of course, as they do, was pass responsibility onto the BBC.
"That is regrettable. We as a council should make it quite clear that we support free TV licences for the over 75s.
"I'd ask council to consider whether or not we start a petition and open up County Hall and Town Hall for members of the public to come in and sign it."
But Conservative councillor Gill Cruise claimed the BBC was to blame, and accused the corporation of "being greedy" and paying executives "fatcat salaries".
Her leader, Coun Nadeem Ahmed said: "I think it's important to remember it's not the Conservative government that's doing this, it's the BBC.
"The days of watching four channels on TV are over. A TV tax is what I call it.
"I don't think anyone should pay to watch TV.
"The BBC should fund itself by advertising, go to the free market and do it that way."
Local Democracy Reporting Service