Speaking in a video statement flanked by several top field commanders of the FSA's Supreme Military Council, the sacked rebel chief said: "We... Have been asked to start working on a total restructuring of the SMC."
Idriss lashed out at the opposition's defence minister, Assaad Mustafa, who reportedly backed his replacement on Sunday by Brigadier General Abdel Ilah al-Bashir.
He described Mustafa's decisions as "improvised and individual."
With the alleged backing of Mustafa and opposition chief Ahmad Jarba, the FSA's larger Higher Military Council had on Sunday replaced Idriss, citing the "difficulties faced by the Syrian revolution" in its battle with the regime.
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"We consider the removal of... Idriss an invalid, illegitimate decision," said a statement issued by all five top field commanders of the SMC, which Idriss had led from December 2012.
They vowed to continue fighting President Bashar al-Assad's regime "under the leadership" of Idriss who was "elected democratically".
Idriss had been voted in by military councils on the ground.
Speaking to AFP on condition of anonymity, a well-connected rebel in Syria said Idriss's removal was decided in a "secret meeting" of the Higher Military Council, which many key rebels have abandoned in recent months.
"The main problem is: why weren't all the military councils called in to vote?"
Idriss had long faced criticism by rebels on the ground for failing to secure more weapons from foreign backers.
But an FSA source told AFP that it was not Idriss's fault that foreign governments had chosen to channel the bulk of their support directly to rebel units on the ground rather than through him.
"General Selim Idriss did everything he could to strengthen the (FSA)," the source said, asking not to be identified.