Liverpool's mayor Joe Anderson has been rebailed until February following his arrest earlier this month.
He was arrested on 4 December, along with four other men, on suspicion of conspiracy to commit bribery and witness intimidation.
The year-long investigation, Operation Aloft, has focused on a number of building and development contracts in the city.
He was initially released on police bail.
Merseyside Police said all five men, including Derek Hatton the former deputy leader of the council, have been rebailed until 19 February.
Following his arrest, Mr Anderson said he was "stepping away from decision-making" and would take unpaid leave while the police investigation continued.
The Labour Party also suspended Mr Anderson pending the outcome of the case.
The father of four was elected mayor of Liverpool in 2012, having served on the city council since 1998.