Prime Minister Benjamin Netanyahu was expected in the coming days to cede the four ministerial positions he holds, following his indictment by Attorney General Avichai Mandelblit in three corruption cases.
According to a Supreme Court precedent from 1993, any government minister under indictment must resign - or be fired if they refuse to do so.
Netanyahu, a four-term conservative leader, has denied the charges of bribery, fraud and breach of trust and said he will stay in office and defend himself.
Netanyahu is currently serving as acting agriculture minister, health minister, Diaspora affairs minister, and welfare minister.
The precedent does not apply to the prime minister, but calls have already been made for Netanyahu to step down out of moral obligation.
The Blue and White party on Friday called for Netanyahu to resign his ministries, also citing this precedent, and a watchdog group asked the Supreme Court on Sunday to order Netanyahu to step aside.
In its petition to the Supreme Court, the Movement for Quality Government in Israel said the first-ever criminal charges against a sitting Israeli prime minister constituted "the crossing of a red line and a grave blow to public trust in ruling institutions."
For now, however, pundits say that Netanyahu will not resign his position as prime minister.
Netanyahu is expected to hand his remaining ministerial positions to other MKs or Likud ministers, which could have a profound influence on snap primaries the Likud party could hold in the coming weeks.
Among those expected to receive a ministry are Deputy Foreign Minister Tzipi Hotovely, chairman of the Knesset Foreign Affairs and Defense Committee Avi Dichter and Likud MKs Sharren Haskel, Yoav Kisch and David Bitan.
Deputy Health Minister Yaakov Litzman of the ultra-Orthodox United Torah Judaism party is expected to become the minister of health if Netanyahu forfeits that portfolio.
The party's Council of Torah Sages, its main decision-making apparatus, approved this measure on Saturday.
In UTJ, there is concern however that Litzman himself might be indicted in two separate cases and will also have to resign.
The first case is a sex abuse scandal in Australia, in which Melbourne headteacher Malka Liefer sexually abused several underage female students at an Orthodox Jewish school and was helped to flee to Israel to escape charges, allegedly under Litzman's order.
Three months ago, police officials stated that is evidence against Litzman to charge him with fraud and breach of trust in the case.
The second is a case in which Litzman faces charges of fraud, breach of trust and bribery for allegedly trying to bypass the decision to close a Jerusalem restaurant he frequents after salmonella and listeria were found at the location's kitchen.
Likud MK Gideon Sa'ar, seen as Netayahu's main rival for the party leadership, told Channel 13 on Saturday that the prime minister branding the decision to indict him an "attempted coup," was irresponsible and had a deleterious impact the functioning of the state apparatus."
Sa'ar also lashed out at the prime minister for his failure to cobble together a coalition government, both after the April and the September elections and demanded a snap leadership election.
"Netanyahu couldn't form a government. We need to go to snap primaries in the next 21 days," Sa'ar said.
"We are a democratic party. The Likud hasn't had primaries for years now. I can form a government and unite the state and the political system", he said.
The chairman of the Likud Central Committee Haim Katz said that, "If there are candidates who want to run, they have the option to do so."
The Associated Press contributed to this report