Ferrari team principal Stefano Domenicali (pictured) has been one of the biggest supporters of cost-restriction in Formula One. Reuters.
Five of the group said they wouldn't buy Formula One shares, despite high profits reportedly enjoyed by the governing body, while the sixth, Lotus team owner and businessman Gerard Lopez, reserved judgement.
McLaren team principal Martin Whitmarsh said some teams among the 12 racing this season were battling to stave off extinction, making it crucial that rival outfits quickly decide how to keep costs down.
"The fact is at the moment, we all know in this room that there's a lot of Formula One teams that are struggling to survive," Whitmarsh told a press conference after practice for this weekend's Malaysian Grand Prix.
"Which tells us we're not doing enough and that's why we've got to keep pushing it."
Ferrari chief Stefano Domenicali called it a "critical" time for many of the Europe-based teams.
"Thank God that our (Ferrari's) situation is very good in terms of our financial position for the future. But we know that the situation of Formula One is not so stable," Domenicali said.
"We know that there's a lot of struggle around so we need to put aside our self-interest a little bit to make sure that we can look ahead. Because this is a very critical period where... we know that it's very tough."
Reports broke last weekend that billionaire Ecclestone was considering a share flotation, possibly in Singapore, as part of talks for a new agreement on how profits are divided between teams and other stakeholders.
Meanwhile, team operators and race organisers alike are warning of financial problems. The Korean Grand Prix is lobbying hard for a cheaper contract and Australia is also reported to suffer multi-million dollars losses each year.
Red Bull's Christian Horner, whose team hold the constructors' and drivers' titles, defended his opposition to new spending restrictions supported by most other teams which would be policed by the sport's governing body.
"Hopefully with some productive discussion going forward a solution can be found to make Formula One cost-control for the top teams, but also make it affordable for the teams in the middle of the grid and at the back of the grid," he said.
"The cost of being competitive in Formula One at present is too high. I don't think anyone will dispute that. The debate is how we achieve it."
Japanese car-makers Honda, Toyota and BMW all withdrew from Formula One during the 2008-2009 financial crisis.