"This is a moment for civic action, collective responsibility, and leadership", said Bishop Dr Desmond Jaddoo, speaking in support of a protest planned later this month.
Unite members started striking on 6 January 2025, moving to an all-out strike on 11 March, leading to piles of uncollected waste in the streets.
Unite said industrial action would continue until a fair deal was agreed with Birmingham City Council. This week, the authority said that despite the strike it would press ahead with a move to fortnightly rubbish collections in the summer.
Jaddoo told the BBC he was "deeply disappointed" the strikes had continued into a second year and that the situation had deteriorated further.
"I warned from the outset that without meaningful dialogue and early intervention, a strike was inevitable," he said.
"Waste collection is not an optional extra, it is a fundamental public service.
"Yet instead of addressing this failure, the council is attempting to introduce additional collections when it cannot even reliably collect recycling. This approach lacks credibility and accountability."
When bin collections move to a fortnightly service, the council aims to reintroduce recycling services, including weekly food waste collections.
A "clean our city" rally is planned to take place on 27 January outside Birmingham Council House at 12:30 GMT, ahead of the full council meeting.
The bishop said: "This situation can no longer be tolerated.
"This is not the Birmingham we want. It is not the Birmingham our residents deserve, and it is certainly not the Birmingham we should be handing on to future generations.
"Workers deserve respect, residents deserve reliable services, and council taxpayers deserve value for money, transparency, and accountability."
'Made multiple offers'
Referring to operations to clear the streets of Christmas waste, the city council said 1,753 tonnes of waste was collected at kerbside on 29 December.
It said voluntary redundancies meant there were now 275 union members taking industrial action as opposed to 370 at the beginning of 2025.
Councillor Majid Mahmood recently told the BBC that waste collections had improved in recent months, although recycling remained suspended, as it has been since industrial action began.
He said the council would also be recruiting staff for its new food waste collection service, which is set to be rolled out from June, alongside the previous recycling service.
"We've been negotiating with Unite now for 12 months and we've made multiple offers, fair and reasonable offers to Unite, all of which have been rejected," he said.
Talks to end the dispute broke down early in the summer of 2025, with the council announcing in July it was pressing ahead with its restructuring plans.
But Unite said members are staying "rock solid" on their industrial action.
In a statement, the union said: "There will be no end to the strikes, until there's a fair deal for Birmingham's bin workers."