Asked if shutting down Al Jazeera's operations would make Israel appear to oppose freedom of the press, an official close to the prime minister said the country accepted diverse opinions but not incitement.
The broadcaster "will follow up the subject through appropriate legal and judicial procedures", he added.
Israel plans to shut down Al Jazeera's Jerusalem office, stop transmitting its broadcasts and strip the Qatar-based channel's journalists of their credentials, the country's communications minister said Sunday.
Al-Jazeera, a pan-Arab satellite network funded by the Qatari government, already has been targeted by Arab nations now isolating Qatar as part of a months-long political dispute over Doha's politics and alleged support for extremists.
He said it is "delusional" that Arab states in the region banned the news network for that reason but Israel has not.
Kara, of Netanyahu's Likud party, said he wants to revoke press cards from al-Jazeera reporters, which in effect would prevent them from working in Israel.
The ministry added that it had become "ridiculous that the channel continued to broadcast from Israel".
"Al Jazeera stresses that it will closely watch the developments that may result from the Israeli decision, and will take the necessary legal measures towards it. Al Jazeera will continue to cover the events of occupied Palestinian territories professionally and accurately, according to the standers set by worldwide agencies such as the United Kingdom office of Communications".
The logo of Qatar-based Al-Jazeera network is seen in one of their offices in Jerusalem June 13, 2017.
Al Jazeera has fiercely defended its reputation and says it is independent.
"We have identified media outlets that do not serve freedom of speech but endanger the security of Israel's citizens, and the main instrument has been Al Jazeera", Kara said.
Israel has, however, frequently accused it of being biased in reporting the Israel-Palestinian conflict. A Palestinian also broke into a home in a Jewish settlement in the West Bank and stabbed four Israelis, killing three of them. Under a decades-old agreement, only Muslims are allowed to pray inside the Al-Aqsa mosque compound, although anyone can visit, including Jews.