A meeting of the full council has been called to settle the leadership issue
Doncaster Council is holding an extraordinary meeting after a row erupted over the appointment of a new interim chief executive.
Councillors voted last month to appoint Tim Leader to replace Paul Hart who had resigned for "personal reasons".
But mayor Peter Davies then wrote to Mr Leader, claiming his appointment was legally flawed and urging him to quit.
There were a series of heated exchanges as the meeting, which began at 1400 GMT, continued into the evening.
The leadership crisis comes after the council was criticised over torture attacks by two brothers in Edlington.
The boys, aged 11 and 12, were given indeterminate sentences last month for torturing two other boys, aged nine and 11, in the South Yorkshire village last April.
A serious case review found the attacks had been "preventable".
The council's children's services department is now being run by the government after the deaths of seven children in the town between 2004 and 2008.
Meanwhile, the Audit Commission is set to carry out a snap inspection of the local authority because of "serious concerns about the council's performance in the last two years".
The controversy over the appointment of Mr Leader as interim chief executive was made public when a letter from Mr Leader to Mr Davies was seen by BBC News.
It revealed the mayor told him he had consulted lawyers and believed his appointment was "legally flawed".
Mr Davies is said to be unhappy over Mr Leader's appointment
In the letter, Mr Leader said the mayor had told him that neither he nor the cabinet had any confidence in him and that he should "resign forthwith".
Mr Leader said he would be happy to discuss the "difficulties that have arisen".
"I shall not, however, be forced from my post by a peremptory, improper, unfair and wholly unjustified demand for my resignation," he said.
In a statement Doncaster Council said: "It is a matter of public record that there has been some controversy regarding the council meeting that took place on 18 January and the decision to appoint an acting chief executive.
"Following the receipt of specialist legal advice it has become clear that a further meeting of the council will be required to conclude the process."