Birmingham City Council will not be taken over for the foreseeable future, the Government has decided.
Local Government Secretary Greg Clark said the authority had improved and he would ask a government-appointed panel, which has been reporting on the authority's progress, to "step back".
It means the threat of Mr Clark sending in officials to take over the authority has been lifted for now.
But there is still doubt about the council's ability to cope with massive spending cuts, with a team of experts saying they have "cause for concern" about plans to slash staffing costs in the authority by £18 million and to cut spending on adult social care by £30 million.
In a joint statement, Birmingham City Council's Labour leader John Clancy and the leaders of the city's Conservative and Liberal Democrat groups vowed to continue making improvements.
They said: "We accept there is still more work to be done and at a faster pace."
It follows a damning report in December 2014 by former top civil servant Bob Kerslake, which warned Birmingham was failing to get "basic services" such as street cleaning and bin collection right.
The Government gave the city 12 months to improve - and later extended the deadline to March this year - and appointed a panel of experts to check on whether it was making enough progress.
If it failed, then options included breaking up the authority into smaller councils and sending government inspectors to take it over.
But the latest report by the Birmingham Independent Improvement Panel, chaired by business leader John Crabtree, has concluded that progress is being made.
The panel said: "The change in the council's political leadership in December 2015 marked a significant point in the council's ability to move forward with its improvement programme."
And it said the council should have a chance to continue making improvements without the current level of intervention.
But the panel said there was a "clear risk" the council would not be able to make all the spending cuts it required to stay within its budget.
Speaking in the House of Commons, Mr Clark said he had agreed the improvement panel would stop making reports to him on the council's progress until the autumn.
But he warned: "There remain a number of challenges that the council will have to overcome."
Coun Clancy, for the controlling Labour group, Conservative group leader Robert Alden and Liberal Democrat group leader Jon Hunt said in a joint statement: "The panel has stated we must build further momentum - and that is precisely our intention.
"We accept there is still more work to be done and at a faster pace.
"Therefore, we have no intention of taking our foot off the gas and we will be concentrating on ensuring sustained change across the whole organisation and, more importantly, delivering the best quality services and outcomes for our residents.
"There is a collective commitment to restore the city council's reputation and help Birmingham realise its full potential, working with partners across all areas to continue this pace of change and improvement."