They then banned Al Jazeera in their territories, and demanded it be shuttered as one of the conditions to mend fences.
Prime Minister Benjamin Netanyahu wrote on Facebook that he wanted the network expelled amid tensions over a holy site in Jerusalem.
Communications minister Kara said cable TV providers had agreed to take the network off the air, but that closing its Jerusalem bureau would take time "Al Jazeera has become the main tool of Daesh [the Islamic State group], Hamas, Hezbollah and Iran", he told a news conference.
Al Jazeera says Mr Kara's comments are unsubstantiated and it will take legal action if Israel acts on its threat.
Israel's move follows in the footsteps of four Arab countries that are aligned against Qatar as part of a months-long political dispute. Others, including the United Arab Emirates and Bahrain, have blocked its channel and websites. Netanyahu has blamed Al Jazeera for stirring passions against Israel that recently led to violent Palestinian demonstrations at a contested Jerusalem shrine. Defense Minister Avigdor Lieberman has likened its coverage to "Nazi Germany-style" propaganda.
The ministry added that it had become "ridiculous that the channel continued to broadcast from Israel". Al Jazeera said in a statement late on Sunday.
A decision will be made after receiving that opinion, he said.
Journalists working for the pan-Arab station in Israel weren't expecting imminent moves against them. It said it will study the issue and decide how to proceed.
New York-based group The Committee to Protect Journalists also criticised the move, which it called "undemocratic".
Israel has long boasted of being a bastion of press freedom in the Middle East and pointed to Al Jazeera's presence in Jerusalem as proof.
CPJ was responding to a report on Al Jazeera that there was an effort to close its offices in Jerusalem and revoke its journalists' credentials.
Hamas, the Islamic militant group that rules Gaza, condemned the move.
'Al Jazeera had a big role conveying the Palestinian narrative with a high professionalism, ' said spokesman Hazem Qassem.
American viewers became familiar with Al-Jazeera after the attacks of September 11, 2001, when its golden-hued Arabic logo became synonymous with video messages by al-Qaida leader Osama bin Laden.
Israeli commentators have pointed out that shutting down Al Jazeera in Israel anytime soon is highly unlikely since this requires a long process in parliament, which is now on break and where the move would face stiff objections.