But key coalition partners have vowed to stand by the veteran leader for now, pending a decision by the attorney general whether or not to indict him.
A decision could take months and Mr Netanyahu claimed his government would be “stable” for the time being.
He said: “I want to reassure you, the coalition is stable.
“We will continue to work with you for the good of Israel’s citizens until the end of the term.”
Both claims against Mr Netanyahu, which the leader denies, represent one of the biggest challenges to his long dominance of Israeli politics.
But Defence Minister Avigdor Lieberman, who heads the ultra-nationalist Yisrael Beitenu party, said that as long as Mr Netanyahu was not convicted he should stay in office.
He said: ”Truly, right now we are operating in a very synchronised way.
“There is no place here for manoeuvring, for any other considerations.”
Education Minister Naftali Bennett, who heads the right-wing Jewish Home party, said: “I have decided to wait until the decision of the attorney general.
“Regarding the moral aspect, the public will decide on voting day.”
One of the cases against Mr Netanyahu alleges the “committing of crimes of bribery, fraud and breach of trust”.
Claims include the leader accepted gifts including champagne, cigars and jewellery worth more than one million Israeli shekels (£204,000)
Any legal proceedings would probably focus on whether political favours were sought or granted.
The second investigation alleges “bribery, fraud and breach of trust by the prime minister” relating to his dealings with the publisher of an Israeli newspaper.
Signalling business as usual, Mr Netanyahu has not changed his plan to attend the annual Munich security conference that begins on Friday.