The meeting follows a devastating defeat in the elections held by the party's central committee. Feiglin, who heads the Jewish Leadership Movement, is also considering starting his own political party along with his supporters from the Likud.
It was not the first time Feiglin has considered leaving the Likud, but at every previous meeting it was decided that he would continue leading the party's right wing.
Feiglin has been a thorn in the sides of two consecutive prime ministers, Ariel Sharon and the Benjamin Netanyahu, who ended up battling him in different ways, including attempting to remove his name from the party roster.
Netanyahu dislikes Feiglin's supporters because they create a hawkish image for the already right-wing party. Before the recent elections he campaigned against the movement in order to ensure their stance did not gather support.
The prime minister personally held a number of conferences in order to bring party members to his side from that of his adversary.
Feiglin's affiliates said he may resign, but that this was a mere possibility at this point. Many members of the Likud said he was hit hard in the elections, and Feiglin himself was even seen to shed a tear before the television cameras that covered the event.