“Today we shall hear arguments on the question of bestowing the duty of forming a government on a Knesset (Parliament) member against whom an indictment has been filed," Chief Justice Esther Hayut said as she opened proceedings.
The court will also hear petitions challenging a coalition deal the premier made with his former rival Benny Gantz.
"Tomorrow there will be a hearing on the second issue, regarding the coalition agreement," Hayut added.
Netanyahu and Gantz reached an agreement last month to form a ruling coalition. The deal between the two men states they will take turns in governing the country after three elections in less than a year failed to bring one of them to power.
Under their agreement, which is supported by a majority in the Knesset, right-wing Netanyahu will continue to serve as prime minister for 18 months before passing the role to Gantz.
Gantz had vowed during his campaigns that he would never sit in a government led by a PM facing corruption charges. But the former general changed his position due to the gravity of the coronavirus crisis, he said.
His decision outraged most of his political allies who split from the Blue and White party, an alliance he established one year ago with the aim of defeating Netanyahu.
Opposition parties and democracy watchdogs requested the supreme court to declare the new political agreement illegal and to bar Netanyahu, who faces a criminal trial on corruption charges, from remaining in power.
Israel’s longest-serving PM, Netanyahu denies any wrongdoing and claims he is a victim of a political witch-hunt.
The state’s Attorney General Avichai Mandelblit, who had indicted him, said in a message to the court, that there was no sufficient legal ground to disqualify Netanyahu.
He described the case as a “head-on collision” between “on one side the most basic democratic principle of honoring the will of the majority ... (and) on the other integrity in public service, specifically among elected officials.”
Wearing face masks and separated by screens, eleven judges presided the hearing, while a group outside the court, also following social distancing indications to limit the spread of COVID-19, carried signs and Israeli flags in protest against government corruption.
"The very fact that we even need to discuss the obvious issue - a criminally-charged man forming a government is already a failure, it's already abnormal," a demonstrator told AFP.
"Would you hire someone who is criminally charged? No. You wouldn't even let him be the school janitor.”
As the court’s decision is expected to be announced later this week, some Israeli analysts said it was unlikely it would bar the PM from leading a new government. The country’s law stipulates a prime minister under indictment is not obligated to step down until a final conviction.
A ruling against the premier would trigger a fourth election, a scenario that most Israelis would rather avoid, especially at a time when the country is facing the coronavirus crisis and its economic effects.