Councillor Rajbir Singh, leader of Sandwell Council, said he would urge Ministers to "not punish the poorest" over the end to the £20-a-week increase.
But Councillor Jay Anandou, deputy leader of the Conservatives, dismissed the move and said nothing was likely to happen as a result of the letter.
He argued the increase was only ever a temporary measure – and said the council's Labour leadership needed to do more to tackle deprivation in the borough.
Councillor Singh, who was critical of the move to end the benefit increase on October 6, said: "With spiralling energy prices, soaring food and living costs and the end of furlough, now is not the time to reduce over £1,000 per year from our lowest income families.
"If the Government does not reconsider its action many people will be left in the unacceptable position of having to choose whether to heat or eat this winter, to be followed by a spring in which workers will also be hit with an increase in National Insurance.
"As a society, we cannot expect the heaviest burdens to be shouldered by the most vulnerable, I urge the Government to see sense and not punish the poorest in our community."
A motion was proposed at the council meeting on Tuesday by environment cabinet member Councillor Ahmad Bostan, who said it was "not the time simply for slogans and words, but for real actions".
However, Councillor Anandou said the Labour-run authority was to blame for deprivation in Sandwell, not Governments,
He said: "Sandwell has been one-party for the last 47 years. They've been in complete control over business rates, the taxpayers' money and providing services to the local people.
"There's a recent index by the Legatum Institute and they've ranked local authorities by key performance indicators and in almost all, Sandwell is in the bottom 20 or in the bottom 10 out of 379 councils.
"We've had nine Prime Ministers – from [Harold] Wilson to Boris Johnson and we've had at least three Labour Governments and mostly Conservative [over the past 47 years]. Are we going to blame them for Sandwell's deprivation?
"It's Labour who hold the pen on Sandwell all along, they have absolute authority. They [are in charge] of adult services, children's services and they in the bottom of the table. The council leader is writing a letter – this is a political stunt, nothing is going to happen."
Councillor Anandou said the authority also needed to sort the problem of its management as he cited Providence Place in West Bromwich, which resulted in a loss of £22.5 million to the taxpayer when it was sold off.