The Green Party has asked Labour councillors to help review the budget for Brighton and Hove City Council for the current year.
Green councillors want their Labour rivals as well as unions and representatives of the voluntary sector to look again at the council’s finances.
Both political parties worked together to make some amendments to the budget passed in March when the council was being run by the Conservatives.
Despite the amendments, the council voted to make £32 million cuts to local services.
Now the Greens are the largest party in Brighton and Hove – after the local elections held last Thursday (5 May) – they want to see whether more changes are possible.
The party lacks a majority so would need to be able to count on Labour backing to vote through any changes.
In a message to Labour councillors, Green group convenor Bill Randall said: “Will you support us in reviewing the 2011-12 budget to see if we can stop some of the cuts that will harm frontline services in Brighton and Hove?”
At the weekend the Brighton and Hove Labour group leader Gill Mitchell ruled out working in coalition with the Greens saying that they deserved a chance to go it alone as a minority administration.