Badran said outlawing the Islamic Movement would be certain to escalate tensions and clashes in Jerusalem and elsewhere.
Israel's domestic security service, the Shin Bet, is reported to have made a similar assessment.
Last week, Salah denounced what he called "unbridled incitement" against his wing of the movement, adding: "We will not yield to threats intended to cow supporters of Jerusalem and al-Aqsa."
Zeki Aghbaria, a spokesman for the movement, told Middle East Eye: "Netanyahu has no authority to decide anything at al-Aqsa. We will continue the struggle to defend it whatever he decides."
Last month, Israel also banned the Mourabitoun, a cadre of Islamic students based at the mosque. Clashes in the Old City and neighbourhoods of East Jerusalem increased dramatically in the days after the ban was imposed.
The group, which enjoys close ties to the northern Islamic Movement, has repeatedly confronted Jewish ultra-nationalists who also stake a claim to the site.
Salah and his followers believe Israel wishes to encroach on Islamic sovereignty at al-Aqsa so that the compound can be divided between Muslims and Jews, as occurred in the 1990s at the Ibrahimi mosque in Hebron.
"Hysterical aggression"In an apparent reference to the Islamic Movement during his speech at the Knesset's opening on Monday, Netanyahu said Israel's "enemies" were "using mendacious propaganda about Temple Mount to make trouble."
Underscoring his demand that Zoabi be tried for incitement, he accused her of calling for "wholesale terror against Israeli citizens."
Zoabi told MEE Netanyahu had twisted her comments to suggest she was calling for an armed struggle. "I was arguing the opposite: that Palestinians in the occupied territories need to concentrate on a popular, non-violent intifada as a way to raise their morale and liberate themselves.
"The stabbings we see every day are an expression of individual Palestinians' sense of frustration and hopelessness. The attacks will end when Palestinians collectively find a better way to resist."
Of the attacks on her and the Islamic Movement, she said: "Netanyahu is falling back on his favorite trick -- creating an enemy to generate fear among his followers. He has lost the issue of Iran, so now he needs me and the Islamic Movement.
"His hysterical aggression really reflects the fact that he is growing ever more politically impotent."
Comparison with Islamic StateGhanem said the Israeli prime minister had sought to blur the differences between Salah's movement, which disavows violence, and militant groups in the region.
Netanyahu has compared the northern movement both to Hamas, which fights Israel through its military wing, and to Islamic State, which has been leading violent campaign through Iraq and Syria, and has been linked to two large-scale suicide attacks in Turkey.
Ghanem said the Islamic Movement's policies had not changed in the past 20 years. "They do not call for violence. They live in Israel and accept they must work within the laws."
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