Ehud Barak's resignation caught Peretz, Cabel, Majadele and Ben-Simon by surprise after they had tried to split off from Labor for months.
Four Labor MKs - Amir Peretz, Eitan Cabel, Raleb Majadele and Daniel Ben-Simon announced on Tuesday that they would remain in the Labor Party, a day after Defense Minister Ehud Barak announced that he was stepping down as the party chairman and forming a new faction Atzmaut.
Barak announced on Monday that he was stepping down as Labor Party chairman to set up a new party, following months of turmoil within the weakened faction.
After Barak's announcement, all of the Labor Party's remaining ministers decided to exit the government. The ministers' resignations will become valid on Wednesday.
"I do not plan to speak extensively on Barak's opportunism, in which his personal interests were more important to him than the national interests," Peretz said during a press conference on Tuesday.
"We will not agree to any move that will be made without coordination and agreement," he added.
"We will hold the talks immediately, out of the hope that we will find common ground," he said regarding the remaining members of the Labor Party.
Barak's resignation on Monday caught Peretz, Cabel, Majadele and Ben-Simon - who have come to be known as the "four" - by surprise. For months they had tried to split off from Labor but failed to find a fifth MK required to do so.
The four said in a press conference that they decided that they would remain in the Labor Party, alongside Avishay Braverman, Isaac Herzog and Benjamin Ben-Eliezer, who resigned as Labor ministers.
Including the four, Labor currently has eight remaining MKs.
Earlier, Barak and Prime Minister Benjamin Netanyahu agreed after intense negotiations that the new Atzmaut faction formed by Barak would receive four portfolios in the current coalition government.
The four Labor ministers who resigned following Barak's resignation on Monday will be replaced by MK's who have joined Barak's new faction.
Barak will remain the defense minister, MK Shalom Simhon will be appointed the new National Infrastructure Minister replacing resigning Labor minister Benjamin Ben-Eliezer, MK Matan Vilnai will receive the Minority Affairs portfolio replacing Avishay Braverman, and MK Orit Noked will be appointed the new agriculture minister, Simhon's former position.
Netanyahu will take over the welfare portfolio, which had been held by resigning Labor minister Isaac Herzog.