Mr. Netanyahu himself was absent from Monday’s parliament vote, which dominated newspaper headlines and radio talk shows.
A government spokesman on Tuesday said Mr. Netanyahu was absent because of a mourning ritual for his recently deceased father-in-law.
Commentators, however, questioned whether he was trying to avoid criticism over the measures, which have caused a furor not only among government opponents but within Mr. Netanyahu’s coalition as well.
One of the two bills would change the way the top court’s judges are selected; the other would change the rules for becoming chief justice.
Both proposals, which require further votes in parliament to become law, would let officials influence who joins the court next.
Critics of the Supreme Court say it is too activist and biased and usurps the legislature’s power.
• From wire dispatches and staff reports