"Force India was very encouraged by the meeting and was appreciative of the FIA (International Automobile Federation) responding so positively to the letter that was sent," that team's deputy principal Bob Fernley told Reuters.
"We are optimistic that following the Biggin Hill meeting a constructive process will now take place."
Force India, Sauber, Caterham and Marussia wrote to the FIA last month when the governing body announced that a planned cost cap for 2015 had been scrapped because leading teams were opposed to it.
The cap had been previously agreed unanimously by all 11 teams, who attended Thursday's meeting along with the FIA and commercial supremo Bernie Ecclestone, and the U-turn angered those struggling to compete on a fraction of the budgets enjoyed by the wealthiest.
Formula One set up a Strategy Group last year with champions Red Bull, Ferrari, McLaren, Mercedes and Williams as permanent members and Lotus as best of the rest.
The Group replaced a Sporting and Technical Working Group, that had included all 11 teams, with the aim of streamlining decision-making.
Critics say it effectively disenfranchises the smaller teams, who could previously have blocked changes under a requirement for unanimity, and concentrates power in the hands of the wealthy elite.
The smaller teams had also suggested in their letter to the FIA that the situation could be brought to the attention of the European Union's Competition Authority as "an abuse of a dominant position".
"It is becoming more and more apparent that the current governance structure adopted within Formula One substantially favours certain teams over others," they had said in that document.
Fernley said the upshot of Thursday's meeting was to put the sport "back on track to re-look at cost controls", even if a cap was unlikely to be revived, with more meetings to be scheduled.
(Editing by Ed Osmond)
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