Demonstrators fear the proposed reforms, which would increase the power of politicians over the courts and are already moving through parliament, are a threat to Israeli democracy.
Israel's allies abroad have also raised concerns about the overhaul.
Tens of thousands of Israelis protested in Tel Aviv and other cities, according to crowd estimates by Israeli media.
Similar-sized crowds have taken to the streets on other occasions during routine protests over the past few months since the proposals were introduced.
Netanyahu, in a televised address, said he was determined to advance the reforms but wanted to reach a solution acceptable to both supporters and critics of the proposal.
"The opponents of the reform are not traitors. Partisans are not fascists," he said.
"I will do everything, everything, to bring calm and end division among the people" after months of protest, including objections from high-level officials.
Defence Minister Yoav Gallant, who has backed calls to pause the legislative process for dialogue with its opponents, cancelled a planned address to the nation on Thursday evening after a meeting with Netanyahu, shortly before the premier went on TV.
Lawmakers earlier on Thursday approved legislation restricting grounds for declaring a premier unfit for office, a move opposition chief Yair Lapid called "a personal law" to protect Netanyahu, who is on trial for corruption which he denies.
Last week, President Isaac Herzog, who holds a largely symbolic role, expressed concern over the deepening rift in society and presented a proposed compromise. The government rejected it.
"Anyone who thinks that a genuine civil war, with human lives, is a line that we could never reach, has no idea what they are talking about," Herzog cautioned.
On Thursday one demonstrator, Nadav Golander, 37, warned of a "dictatorship" if the government presses forward with its agenda.
Many demonstrators carried Israeli flags and some clashed with officers. Police reported at least 10 arrests in Tel Aviv over alleged public order offences.
Thousands also rallied in Jerusalem outside Netanyahu's residence as well as in the northern city of Haifa and southern Beersheba, Israeli media said.
Justice Minister Yariv Levin announced the reforms in January, days after Netanyahu's government took office, a coalition with ultra-Orthodox Jewish and extreme-right allies.
Netanyahu and his allies say the proposed changes are necessary to diminish the powers of the Supreme Court, which they argue has become politicised.
Members of the opposition have refused to negotiate with the coalition, demanding a complete freeze on all legislation related to the judicial reform.
In a call Sunday with Netanyahu, US President Joe Biden voiced support for a "compromise" and stressed the importance of "genuine checks and balances", the White House said.
German Chancellor Olaf Scholz had urged Netanyahu to reconsider Herzog's compromise proposal.
On Monday, the ruling coalition presented an amended version of a key element of the overhaul, ahead of votes planned before parliament goes into recess next week.
Other pieces of legislation in the reform package would wait until the summer session to enable "real dialogue" with the opposition, coalition parties said in a joint statement.
The new version of a bill to change the way judges are selected would put more lawmakers and members of the judiciary in the judicial appointments panel than the initial text.
Opponents have accused Netanyahu of trying to use the reforms to quash possible judgements against him, an accusation he rejects.
Lawmakers on Thursday voted 61 against 47 to approve an amendment to one of Israel's Basic Laws, the country's quasi-constitution, specifying the conditions for temporary removal of a prime minister.
The previous version of the law stated that a premier could be declared incapacitated, but did not specify on what grounds or lay out the necessary steps.
The amended legislation requires a request by the prime minister, or a government vote backed by a three-quarter majority of ministers, and only for mental or physical health reasons.
The law "de facto limits the possibility of declaring a prime minister incapacitated to exercise their functions", said Guy Lurie, a researcher at the Israel Democracy Institute in Jerusalem.
"Reasons other than those specified in the amendment will no longer be admissable," he told AFP.
Some opposition figures and civil society groups have argued for Netanyahu to be declared unfit to serve, citing his ongoing trial. He denies the charges of bribery, fraud and breach of trust.