Israeli Prime Minister Benjamin Netanyahu rejected a compromise on government judicial reforms suggested by the country's President Isaac Herzog on Wednesday.
Organisers say the protests are the largest in Israel's history.
On Wednesday evening, Mr Herzog begged both sides to come together.
"I want to tell you something from the heart and I very much hope that it will penetrate your hearts,” he said.
“In my life, in the worst nightmares, I never thought I would hear such words, even if it is from a very small minority of people.
"I heard startling rhetoric. I hear real, deep hatred. I hear people from all parties say that the idea of blood in the streets no longer shocks them."
Mr Netanyahu then wrote on Twitter that Mr Herzog's measures, which formed a bolder challenge to the government's plan that many had expected, "only perpetuate the existing situation and do not bring the required balance to the Israeli authorities ... this is the unfortunate truth".
In response, protesters across the country are escalating action on Thursday, which includes military reservists blocking access to Haifa's port and demonstrators painting a red line on the street that leads to the Supreme Court in Jerusalem, symbolising the connection between the independent judiciary and democracy.
In a sign of growing resentment over the country's ultra-Orthodox community, demonstrators set up a symbolic military "recruitment centre". The ultra-Orthodox are the only community exempt from military service, which causes resentment among many Israelis.
The most religious parties in Mr Netanyahu's administration say they will not compromise on an overriding clause, part of the legal reforms that would allow the government to overrule court verdicts. They fear it could be used to draft members of the community into the military, which they say is an unacceptable incursion into their religious practices.
Mr Netanyahu's far-right administration also wants to give government more power in choosing judges. The government views the judiciary as too powerful and biased against the right-wing.
Justice Minister Yariv Levin has said the original government plans would give politicians in power more sway over the committee that makes selections.
'Insult to the public'
Mr Herzog's plan proposes a committee comprising three ministers, the high court president, two civil servants and two judges jointly agreed by justice minister and president.
Transportation Minister Miri Regev described the package as “an insult to the intelligence of the public”.
Wednesday's developments threw Mr Netanyahu's international diary into chaos. An official visit to Germany was first curtailed, then postponed due to security situation in Israel.
As his plane departed from Ben Gurion Airport, Mr Netanyahu said the main subject for discussion with German Chancellor Olaf Scholz would be a harsher European stance on Iran, as well as other issues important to Israel.
"The security issues do not take a break, even for a moment," he said.
Protesters attempted to block the airport from which Mr Netanyahu was departing for the second time this month, after an earlier attempt to stop the Prime Minister flying to Italy for another official visit.
His Berlin trip was cut short by continuing Israeli military investigations into whether a mysterious blast in northern Israel on Monday was the work of Lebanese militant group Hezbollah.
The explosion seriously injured one Israeli, with the attacker later shot dead near the Lebanese border, hours after the attack.
Israeli media had previously been banned from reporting details of the incident. The unusual nature of the device has led to suspicions that it had been smuggled from Lebanon.
Israel considers Hezbollah the country's main enemy and threat.
A month-long war between Israel and Hezbollah broke out in the summer of 2006.
Four years ago, Israel discovered what it described as a series of tunnels dug by Hezbollah under the border.
Israel often attacks targets in Syria, which it suspects of allowing a smooth path of arms deliveries from Iran to Hezbollah militants.