Education Minister Naftali Bennett and Justice Minister Ayelet Shaked, both of the far-right Habayit Hayehudi party, are slated to give a televised statement on Monday morning.
A source close to Bennett said that the two might resign from Prime Minister Benjamin Netanyahu's government if the latter doesn't give Bennett the defense portfolio.
Netanyahu on Sunday assumed the defense portfolio following Defense Minister Avigdor Lieberman's resignation last week. His party, Yisrael Beiteinu, is leaving the governing coalition over the cease-fire it had reached with Hamas in Gaza.
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In a statement on Sunday, Netanyahu called on the rest of his coalition partners not to dissolve the government.
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"We are in a particularly complex security situation," Netanyahu said in a press conference. "In times like these, you do not overthrow a government. It's irresponsible. We have another full year until elections."
Agriculture Minister Uri Ariel, a member of Habayit Hayehudi, told Army Radio on Monday that it seems that Bennett and Shaked are expected to announce their resignation.
"I'm working to change this and reach a reality that Bennett is [appointed] defense minister. It's right for the country, right for security and I hope it will work out," Ariel said, noting that he spoke to Bennett about his plans.
On Sunday Bennet told confidants that he "plans to go all the way" if Netanyahu refuses to appoint him defense minister.
However sources in the Habayit Hayehudi said that the televised statement was an attempt by Bennett to pressure Netanyahu into giving him the defense portfolio; it wasn't clear if he in fact plans on resigning from the coalition.