The council was put under special measures last July
A council which is already being run under special measures has been told more needs to be done to improve the way the authority is being run.
Carl Sergeant, the assembly government's local government minister told Anglesey councillors progress had been made.
But he said the council should focus on the real needs of the island, and stop "petty bickering".
Councillors said they were "committed" to "driving the authority forward".
The council was put under special measures by the assembly government last year.
It followed a damning report by the Auditor General for Wales after an inspection revealed weaknesses in the way the council was run.
Mr Sergeant met with members and officials at Anglesey council on Wednesday and told them he would "not hesitate to take further action if improvement is not achieved quickly".
"The council must focus on the real needs of this island and its citizens," he told them.
"Debate too often concentrates on personal and parochial conflicts and rivalries.
"This is a betrayal of Anglesey's citizens and communities, who deserve action and leadership, not petty bickering."
He said misbehaviour had to be dealt with "properly" and "anyone who obstructs recovery must be dealt with".
The standards committee should be overhauled with a remit to raise standards "proactively", and should meet more frequently, he said.
He added that councillors must also become members of the standards committee so that they can contribute to maintaining those standards.
The overview and scrutiny systems also needed "serious re-examination", he said.
The council's recovery board had been asked to monitor developments closely over the next few months, he said.
"I expect to see clear and rapid progress toward their recommendations - otherwise I may be forced to direct you to take action," he added.
The minister said he could establish and dissolve committees, make internal and external appointments, amend the constitution, councillor allowances and arrangements for delegated powers.
He insisted that he did not want to contemplate the consequences of failure.
"Failure to complete the tasks required will drive me to consider the future of the council as an autonomous body.
"Do not force me to go there," he said.
Following the meeting Anglesey council's leader Councillor Clive McGregor, leader of the opposition Councillor John Chorton (Labour), Councillor Bob Parry (Plaid Cymru), Councillor Gareth Winston Roberts (Anglesey Forward) and Councillor Hefin Thomas (Menai Group) issued a joint statement.
They said they remained committed to corporate recovery and driving the authority forward.
"There has already been improvement on several fronts and we are pleased that this has been recognised," the statement said.
"There is patently, however, a great deal we still need to do," it added.
They acknowledged the "seriousness" of the situation facing the authority, which was not underestimated by any member.
"Today we have received a stark message from the minister - we must change or the consequences for Anglesey will be dire," they said.
Mr McGregor added: "Any councillor who does not want to be part of this process should resign from the council and make way for people who will help to make a difference."