Birmingham City Council said it would start a new waste collection regime in the summer, including a reinstated recycling service, even if strike action continued.
Councillor Majid Mahmood, cabinet member for environment and transport, apologised to residents for the disruption caused by the dispute and said the authority wanted to end it.
“But let us be clear, the council has made a series of offers to Unite to end the strike, but they have all been rejected,” he said.
“My message to those still taking industrial action is simple: Come back to work as I want you to be part of this new and improved service. Our door remains open.”
He claimed Unite were being unreasonable in demanding “significant lump sums” which were “unjustifiable”.
Mahmood added every household got a weekly waste collection, with about 1,370 tonnes collected kerbside every day.