Birmingham City Council has been told it is failing to improve quickly enough six months after a damning report found it was failing to provide basic services and had let down the poorest areas of the city.
A panel set up by the Government said poor leadership by the council's top politicians was holding back attempts to deal with its problems.
And it means the council is in danger of being broken up into two or more smaller authorities, or simply taken over by the Government, which could send in its own officials to manage services.
But the local authority's leader Sir Albert Bore insisted he was "confident" progress was being made.
The latest warning comes from a panel chaired by business leader John Crabtree, a former senior partner of Birmingham law firm Wragge & Co and former president of Birmingham Chamber of Commerce.
He was appointed by the Government in January to monitor the council's attempts to improve but he has now sent a damning assessment to Greg Clarke, the Secretary of State for Communities and Local Government, saying too little has changed in the first six months.
And he warned that the council's leaders "may still not understand the scale of the task".
It follows a report in December by former top civil servant Bob Kerslake which warned Birmingham was failing to get "basic services" such as street cleaning and bin collection right.
Cash had poured into big city centre projects while residents in poorer parts of the city had been left without jobs or skills, Lord Kerslake's report said.
And businesses, community groups and hospitals in the city find the council almost impossible to work with - because it thinks it knows best about everything.
The Government gave Birmingham 12 months to improve, and warned there would be drastic action if it didn't, including potentially breaking up the authority.
But halfway towards the deadline, the Birmingham Independent Improvement Panel, chaired by Mr Crabtree, has warned: "While elements of the plan are on track, there are a number of key areas where there has been less progress than expected."
And it said: "While the panel commends the energy and commitment demonstrated by the chief executive and his team, there remain questions about whether the senior political leadership of the council fully understands the scale of change required.
"We are not yet seeing the radical shifts necessary to address the starkest of Lord Kerslake's criticisms relating to the council's culture."
Where the council is going wrong - and where progress is being made
Mr Crabtree's report says "The senior political leadership of the council, in spite of assertions to the contrary, may still not understand the scale of the task facing the council, and the enormous culture change needed right across the organisation by politicians and staff at all levels if the residents of the City are to be well served.
"We continue to observe a council where the politicians with most influence are focusing too much on the inner political workings of the authority rather than engaging widely and enthusiastically with external partners and the communities of Birmingham."
Getting more senior managers to help the chief executive
The authority agreed to appoint more senior managers in March, "however three months later the roles had still not been advertised".
Doing a better job of telling people what's good about Birmingham
The council says it will have a strategy for doing this in September. "Such delay does not inspire sufficient confidence that the council's key stakeholders will be, or will feel, involved and informed."
Improving the way the council works with other organisations in the city
The council was slow to do this but "very recently there have been more encouraging signs of progress".
Dealing with a massive budget deficit - expected to be £250 million over two years
Progress has been slow but "the council has recently got back on track with the challenging timetable and recognises the intensity of effort now required to achieve the planned multi-year programme of service reform".
Drawing up an improvement plan and ensuring the council has the right staff
It is "encouraging" that progress is being made.
Birmingham City Council leader Sir Albert Bore and chief executive Mark Rogers said in a joint statement: "We accept that the council has taken some time to get out of the starting blocks in a number of areas but we are confident that we are now moving forward at pace and on all fronts.
"There will be an acceleration of the actions required over the summer, which will include progressing the recruitment of senior officers to increase strategic capacity; running networking events with partners to develop a shared and long-term vision for the city; and completing a programme of workshops across all service areas to develop our financial planning for both the short and longer term.
"We are pleased that the panel has recognised 'encouraging progress' in relation to member roles and responsibilities in terms of employment and human resources; the reworking of district committee responsibilities; the reduction of scrutiny committees; the alignment of the Leader's Policy Statement and Future Council programme; and the creation of a member development plan that is already being implemented.
"The leadership of the council is fully committed to this programme of wide-ranging a fundamental change and we are pleased the panel has accepted our reassurance on this and that pace will now increase in order for us to demonstrate significant progress by September."