People in Liverpool will be asked whether they still want to have a directly elected city mayor.
Joe Anderson was elected into the newly created role in 2012 but stepped aside recently after being arrested on suspicion of conspiracy to commit bribery and witness intimidation.
The council's ruling Labour group confirmed it would hold a referendum in 2023 on whether to scrap the role.
The Liberal Democrats want a public consultation on alternative models.
But Labour said the coronavirus pandemic made it "impossible" to run any such consultation before May's mayoral elections.
Councillor Dan Barrington outlined a motion to hold a referendum on the mayoral model in 2023 instead.
Lib Dem Councillor Richard Kemp argued many of Liverpool's problems were due to power being concentrated in "one pair of hands".
After the meeting Councillor Kemp said it was "hardly surprising" that Labour had "kicked a consultation into the long grass".
They would "fight to the end" to preserve a mayoral system which "gives many of them large amounts of allowances in a system which is unaccountable to the council as a whole, or the people of Liverpool," he said.
Green Party group leader Tom Crone said it was "a missed opportunity for real meaningful change".
The Labour group, he said, had "denied people that choice and we will be lumbered with a mayor for another three years".
Mr Anderson said he would not fight for re-election in May due to the ongoing police investigation.
He was rebailed until February.
Deputy mayor Wendy Simon is serving asinterim mayor.