FIA President Jean Todt will meet with the teams next month to discuss ways to curb the rising costs of competing in F1.
Last week it emerged that the FIA's proposed budget cap for 2015 would not go ahead as the Strategy Group had opposed it.
The Group - made up of Red Bull, Ferrari, Mercedes, Williams, McLaren, and Lotus - reportedly wrote to Todt informing him that they would not back the plan.
The FIA, though, is adamant that something needs to be done and as such will meet with the teams and Bernie Ecclestone to discuss a way forward.
"The FIA, the Commercial Rights Holder (CRH), and all the F1 Teams have recently confirmed their commitment to work on cost reduction," read an FIA statement.
"Accordingly, the FIA President Jean Todt and the CRH Bernie Ecclestone will organise a meeting with all the F1 Teams on 1 May 2014, followed by a F1 Strategy Group meeting, to clarify the means to achieve a substantial F1 Team cost reduction."