Council leader Lynette Gwyn-Jones has written to her 77 colleagues asking them to reach agreement about how Brighton and Hove should be run.
Last week the leadership's proposal for a referendum on May 3 to decide whether or not Brighton and Hove should have an elected mayor was defeated by six votes.
In her letter, Councillor Gwyn-Jones said the defeat had left the council in a mess, which should be resolved quickly.
Coun Gwyn-Jones hopes to persuade colleagues who voted against the proposals that they still represent the best way forward. Four Labour rebels sided with the opposition to reject the plan.
Coun Gwyn-Jones said consultation carried out by the council, which found half the people were in favour, was thorough and independent.
The letter says: "The only conclusion that could be drawn from this consultation is that we should move forward to the next stage of holding a referendum."
Holding it on May 3 would maximise turnout and save money as it is the expected date of the General Election.
The leader said she had not heard any convincing arguments against holding the referendum on that date.
The letter says: "I am very concerned that an entirely proper process has been agreed by the policy and resources committee and then voted down at council.
"This has created legal confusion and £160,000 to be found from next year's budget.
"The District Auditor has expressed his concern that members be aware that public finances are spent wisely.
"I believe the residents of Brighton and Hove too will find this use of public money hard to justify and the Secretary of State is likely to question the way in which the council seems to be overturning its own processes."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article