The two teams went into administration this month and will not take part in Sunday's United States Grand Prix.
Earlier this year, the FIA abandoned plans for a budget cap after failing to get support from the teams.
But in a statement, the FIA says it remains in favour of any initiative to "help reduce costs".
However, the governing body did not expand on how it planned to do so.
Marussia and Caterham's absence in Austin means only nine teams and 18 cars will be on the grid, the first time that has happened since Monaco in 2005.
On Thursday, the FIA stewards said the two teams were deemed to be in breach of the regulations as they were not participating this weekend.
However, they added that in "view of the teams' current financial circumstances" no penalty will be imposed and have instead referred the matter to FIA president Jean Todt.
Earlier in the day, the FIA said in a statement that the situation would be handled with "extreme care" considering the two teams' current plight.
Former FIA president Max Mosley, whose own plans for a cost cap fell through when he was in office, said this week that the sport could lose more teams because of the high costs of competing.
Further plans to cut costs also failed to materialise earlier this year, but the governing body said it remains committed to finding a solution, especially in light of Marussia's and Caterham's struggles.
"These failings once again acutely raise the question of the economic balance of the Formula 1 championship," added the FIA.
"[They] justify the position, expressed many times by the FIA, in favour of any initiative that will help reduce costs in order to ensure the survival of the existing grid or attract potential new entrants.
"As such, the FIA, in close cooperation with FOM [Formula One Management] and the different stakeholders in F1, will continue to work towards maintaining the attraction of the championship and the equitable participation of the teams in it in the years to come."
United States Grand Prix coverage details
Caterham and Marussia's financial problems highlight the need to cut costs in Formula 1, according to the sport's governing body the FIA.