Israel's parliament, known as the Knesset, will go on recess next week for the Passover holiday.
Earlier in the day, Israel's unions threatened to expand the movement against the judicial reform plans.
"I am calling a general strike," Histadrut chairman Arnon Bar-David said in a televised address, adding that "from the moment this press conference ends, the State of Israel stops".
The Histadrut labour federation, representing hundreds of thousands of workers, issued the ultimatum amid expectations that Netanyahu would be making an announcement regarding the fate of the overhaul.
"Bring back the country's sanity. If you don't announce in a news conference today that you changed your mind, we will go on strike," Bar-David said.
Reporting from Jerusalem, FRANCE 24’s Irris Makler explained that a general strike call is extremely rare in Israel.
“The people have spoken, and today we saw the union movement speaking,” said Makkler, adding that the Histadrut press conference on Monday featured unusual scenes rarely seen in Israel’s history.
“It was quite an interesting press conference because it felt like the protests. People were carrying flags, they were shouting “democratia” – democracy – and the union leaders were flanked by industry leaders,” she said. “It’s a sign that there’s chaos everywhere: teachers’ strike, schools are closed, and now, there’s a potential for a general strike.”
Israeli media reported that takeoffs from Tel Aviv's Ben-Gurion International Airport have been suspended.
Earlier Monday, Israeli President Isaac Herzog urged the government to halt its bitterly contested judicial overhaul
"For the sake of the unity of the people of Israel, for the sake of responsibility, I call on you to stop the legislative process immediately," he said on Twitter.
Herzog’s call followed massive demonstrations over the weekend that saw tens of thousands of protesters take to the streets after Netanyahu fired his defese minister.
Yoav Gallant had spoken out against controversial plans to overhaul the justice system.
As news of the dismissal spread, tens of thousands of protesters, many waving blue and white Israeli flags, took to the streets in Tel Aviv and Jerusalem. Crowds gathered outside Netanyahu's residence in Jerusalem, at one point breaching a security cordon.
Netanyahu's plan to hand more control to politicians and diminish the role of the Supreme Court has regularly ignited protests and been questioned by Israel's top allies, including the US, which expressed concern Sunday.
Critics say the reform project threatens Israel's democracy, but the government argues changes are needed to rebalance powers between lawmakers and the judiciary.
Netanyahu on Sunday decided to "dismiss Defence Minister Yoav Gallant", the prime minister's office said in a brief statement.
In response to the decision, Gallant countered on Twitter: "The security of the State of Israel has always been and will always remain the mission of my life."
Some three months since taking office, Netanyahu's nationalist-religious coalition has been plunged into crisis over the bitter divisions exposed by its flagship judicial overhaul plans.
Gallant's call for a halt to the reforms came as lawmakers are due to vote this coming week on a central part of the proposals, which would change the way judges are appointed.
The US said it was "deeply concerned" about the day's events and called on Israeli leaders to reach a compromise.
The White House noted that President Joe Biden recently told Netanyahu that "democratic values have always been, and must remain, a hallmark of the US-Israel relationship".
"Democratic societies are strengthened by checks and balances, and fundamental changes to a democratic system should be pursued with the broadest possible base of popular support," White House National Security Council spokesperson Adrienne Watson said.
Two other Likud lawmakers tweeted their support for Gallant, raising questions over whether the government could count on a majority if it pushes ahead with a vote.
Opposition leader Yair Lapid said the prime minister could fire Gallant, "but he cannot fire reality and cannot fire the people of Israel who are standing up to the insanity of the coalition.
"The Prime Minister of Israel is a danger to the security of the State of Israel," Lapid added.
Adding to the political uncertainty, Israel's consul general in New York, Asaf Zamir, tendered his resignation Sunday over Netanyahu's "dangerous decision".
"Following today's developments, it is now time for me to join the fight for Israel's future to ensure it remains a beacon of democracy and freedom in the world," Zamir tweeted, posting his resignation letter.
Gallant, a former general, was named to his post in December as part of Netanyahu's coalition with far-right and ultra-Orthodox allies.
He is the first casualty, but other high-level officials have also expressed reservations.
A parliamentary committee amended the draft law to make it more acceptable to opponents, but the opposition has ruled out backing any part of the reform package until all legislative steps are halted.
In a televised address last week, the prime minister vowed to "responsibly advance" the reforms and "end the rift" they have caused in the nation.
In response, Attorney General Gali Baharav-Miara on Friday accused Netanyahu of "illegal" public intervention on the process of adopting the judicial reforms.
Netanyahu is on trial over charges of bribery, fraud and breach of trust, which he denies.
His broadcast gave rise to contempt of court accusations filed with the Supreme Court by the Movement for Quality Government in Israel, a non-governmental, anti-corruption group.
The NGO's complaint alleges Netanyahu violated an agreement with the court that an accused prime minister does not have the right to act in a matter that could constitute a conflict of interest.
Demonstrators have announced a "national paralysis week", including countrywide rallies, protests outside ministers' homes and on Wednesday outside parliament.
(FRANCE 24 with AFP and Reuters)