The teams, two of FOTA's most high-profile members, confirmed their intention to withdraw from the organisation on Friday afternoon, with Ferrari claiming "FOTA's drive has run its course".
Ferrari and Red Bull have been critical of FOTA's failure to bring the teams together in agreement on the sport's Resource Restriction Agreement (RRA), which aims to cap the spiralling costs of competing in the sport.
Both teams insist that they remain committed to helping F1 reduce costs.
"I can confirm this is the case," a FOTA spokeswoman said. "We are trying to arrange a meeting to sit the teams around the table and see where this takes us."
Ferrari outlined their reasons for withdrawing from FOTA in a statement.
"Ferrari has informed FOTA President Martin Whitmarsh that it is leaving the organisation made up of the teams competing in the Formula One World Championship," read the statement on ferrari.com.
"It was a difficult decision and a great deal of thought went into it. It was taken reluctantly after analysing the current situation and the stalemate when it came to debate on some issues that were at the core of why the association was formed.
"Ferrari was on the front line in this area [cost-cutting] even before the birth of FOTA and it intends to continue down this route to ensure the sustainability of the sport in the long term.
"Now, however, it is necessary to find some new impetus to move it along because FOTA's drive has run its course, despite the excellent work of current President Martin Whitmarsh in trying to reach agreement between the various positions for the common good."
Reigning constructors' champions Red Bull also announced their decision to withdraw in a brief statement released.
"Red Bull Racing can confirm it has served notice to withdraw from FOTA," the statement read. "The team will remain committed to finding a solution regarding cost saving in Formula One."
FOTA last season represented 11 of the 12 teams on the F1 grid - backmarkers Hispania Racing are currently the only team not allied with the organisation - and has long been gripped by internal rows over the implementation of the RRA.
Recent talks between team principals at the season-ending Brazilian Grand Prix failed to reach an agreement over a way forward.
Talks could still be resurrected, and with a two-month notice period in force there is scope for Ferrari and Red Bull to reverse their decision should agreement over the RRA be reached.
Ferrari's statement added: "Ferrari will continue to work with the other teams to make the current RRA, Resource Restriction Agreement, aimed at controlling costs, more effective and efficient, modifying it to make it more stringent in key areas such as aerodynamics, to rebalance some aspects such as testing and to expand it to areas currently not covered, such as engines.
"Formula One, like the rest of the world in fact, is currently going through a delicate period. Ferrari wants to work with all parties for the future of a sport that expresses the highest level of motor sport technology."