JERUSALEM -- Israeli leaders proposed harsh new measures Sunday to curb "Jewish terrorism," following a wave of extremist violence that left Israeli and Palestinian children dead in knife and arson attacks.

Shira Banki, 16, an Israeli high school student described by her parents as a sweet and magical child, died of her wounds Sunday after being stabbed by a Jewish extremist at a gay pride parade last week in Jerusalem.

Israelis were reeling from the fast-moving violence of recent days that also included a lethal arson attack in a Palestinian village that left a toddler burned to death.

Defense Minister Moshe Yaalon said Sunday that Israeli authorities should be allowed to employ the same heavy-handed measures against Israeli terrorism suspects as those used against Palestinian suspects in the occupied West Bank, freeing the military to seek "administrative detention" against suspects, which would enable them to hold detainees in prison without charges.

After speaking out against attacks by Jewish extremists and saying he felt shame the violence had come "from my own people," Israeli President Reuven Rivlin was deluged with threats on social media, leading his security detail to file a complaint with Israeli police because of fears that the leader's life was in danger.

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An ultra-Orthodox Jew, Yishai Schlissel, was arrested in connection with Thursday's parade stabbings. He was recently released after 10 years in prison for a similar assault on a 2005 gay pride parade. On Friday, a judge ordered he remain under arrest for 12 days. He has not been charged but could face murder and attempted-murder counts.

On Friday, arsonists set fire to two homes in the Palestinian village of Duma in the West Bank, burning a toddler alive. Authorities say the attack was most likely carried out by Jewish extremists in reaction to Wednesday's clash of Israeli soldiers and police with Jewish settlers over two illegal structures at the West Bank community of Beit El.