McLaren team principal Martin Whitmarsh says Formula 1 teams would like to find a solution to reduce the budgets through dialogue between them and the FIA.
The governing body confirmed on Thursday the introduction of a £40 million budget cap from the 2010 season.
Those teams adhering to it will be allowed more technical freedom, meaning the championship would become a two-tier series, an idea that has been criticised by some of the current teams.
FIA president Max Mosley had said last month that the Formula One Teams' Association's response to the budget cap idea had been "weak", and FOTA said last week its response to the FIA was not ready yet.
The governing body, however, today confirmed the introduction of the cap from 2010 onwards.
While supporting that FIA's push to reduce costs, Whitmarsh suggested teams are unhappy about the idea of a two-tier series.
The McLaren boss insisted dialogue between the teams and the FIA is the solution to find a compromise that would make all parties happy without having two types of cars on the grid.
"As a member of FOTA, Vodafone McLaren Mercedes is of course supportive of FOTA's recent efforts to reduce costs in Formula 1," said Whitmarsh. "Equally, we recognise the excellent work done recently by the FIA in the area of cost-reduction.
"Having said all that, we understand that some teams' operational budgets may still be unnecessarily high in the challenging global economic situation in which we now find ourselves.
"Nonetheless, we believe that the optimal solution - which may or may not include a budget cap, but which ideally would not encompass a two-tier regulatory framework - is most likely to be arrived at via measured negotiation between all parties.
"We at Vodafone McLaren Mercedes are happy to contribute to that process as and when required."