Polls have diverged on public views of the reforms. Channel 13 TV last week found 53% of Israelis were opposed to changing the court appointments' structure while 35% were in support. But Channel 14 TV on Thursday found 61% in favour and 35% opposed.
Critics of the Supreme Court say it is overreaching and unrepresentative of the electorate. Its proponents call the court a means of bringing equilibrium to a fractious society.
"Tens of thousands of people were at tonight's demonstrations. In the election held here two and a half months ago, millions turned out," tweeted Miki Zohar a senior lawmaker in Netanyahu's conservative Likud party.