The meeting was called after the six most powerful teams - Ferrari, Mercedes, Red Bull, McLaren, Lotus and Williams - vetoed Todt's plans to introduce a mandatory budget cap from 2015.
The remaining teams, F1's smallest and least successful outfits Sauber, Force India, Marussia and Caterham, hit back angrily with a letter to Todt alleging that the vetoing 'Strategy Group' may be a breach of Europe's competition laws.
Indeed, the European Commission subsequently confirmed that it is "monitoring" the situation.
The big teams have responded to the crisis by backing instead a range of cost-cutting proposals to the technical and sporting regulations.
International media sources have said the proposals include the extension of paddock curfews, the banning of tyre warmers, and from 2016 and 2017 measures like standardised components, FIA-homologated active suspension, and 18-inch tyre dimensions.
The German news agency DPA claims that, following Thursday's meeting, a "solution" to the divisive issue of urgent cost-cutting now "seems more open".
The report said the small teams intend to respond to the rule change proposals "within the next two weeks".
London's Times newspaper agreed that the threat of a European investigation had eased the crisis between the rebelling small teams and their powerful rivals.
"Todt and the teams are said by insiders to have been rattled by the EU interest and were propelled towards finding a rapid solution," wrote correspondent Kevin Eason.
He added that FIA president Todt "promised to address serious grievances over costs", and vowed to "revive an investigation into the possibility of a team 'cost cap'".
"No one wants to hear that the EU is taking an interest," said a source. "There is the realisation that we have to level the playing field and get costs under control quickly."