Borrell cited "serious concerns about possible breaches of international humanitarian law in Gaza" in a Wednesday letter.
Borrel has been a persistent critic of Israel throughout his term, but in particular in the year since the October 7 massacre.
Katz called Borrell “an antisemitic Israel-hater who leads a campaign against Israel like the greatest antisemites in history.”
The push to advance the idea of sanctions comes as Ben-Gvir had pushed the issue of Jewish prayer on the Temple Mount.
Kaja Kallas supports a two-state-solution and has previously spoken extensively about the humanitarian situation in Gaza.
"The risk of this war effecting the south of Lebanon and spilling over is every day bigger," Borrell told reporters ahead of a foreign ministers meeting in Luxembourg.
Israel's North is still evacuated, Hezbollah is ramping up, and everyone still seems to blame Israel.
"The period of the Hungarian presidency is an unprecedented opportunity to improve Israel's position in the European Union” Katz said.
Borrell and Albanese are promoting the reality that if Israel comes under fire while rescuing its people, it should not shoot back and instead let its soldiers die...
Earlier on Saturday, Borrell also sent remarks congratulating the four hostages on their release, writing on X that they are "are free and safe today."