Liberal Democrat councillors in Birmingham say they will make a legal challenge to the council election results in up to six wards.
Group leader, John Hemming, says he believes there has been fraudulent use of postal votes and is preparing to take the issue to the courts.
No party has overall control of the council following Thursday's election.
Speaking to the BBC, Labour group leader, Sir Albert Bore, criticised Mr Hemming.
He said the election was carried out in accordance with existing guidelines.
But West Midlands Police confirmed on Friday they will investigate allegations of postal ballot fraud after a request was made for 16 ballot papers to be sent to the same address in Sparkhill, Birmingham.
The full result of the election was announced on Sunday night after a second re-count for the Perry Barr ward resumed at the National Indoor Arena, at the same time as the votes for the European elections were counted.
Labour's Lord Mayor-elect, Ron Whitehouse, lost his Perry Barr seat to the Lib Dems, leaving the council with 53 Labour councillors, 39 Conservatives and 28 Lib Dems.
Mr Whitehouse would have taken the mayoralty at the annual council meeting on 29 June.
Former councillor Whitehouse came fifth in a ward where the top three candidates were elected.