Tanks rolled deep into built-up areas in Ramallah
Zeevi's body has been buried at Israel's Mount Herzl cemetery at an emotional ceremony attended by hundreds of mourners.
In the first sign of retaliation for his killing, Israeli forces earlier entered Palestinian-controlled Ramallah and the outskirts of Jenin, where shots fired from an advancing tank hit the classroom of an elementary school, killing 11-year-old Riham Nabil and injuring five others, one seriously.
A police sergeant and a member of Mr Arafat's Force 17 security organisation were shot dead in Ramallah as gunfire erupted after tanks and bulldozers pushed into the town.
In Israeli-occupied East Jerusalem, the Palestinian minister for the city, Ziad Abu Zayyad, said his house and some others had been searched overnight by Israeli police and soldiers with dogs.
The showdown threatens to undercut Washington's efforts to win broad Arab and Muslim support for its military strikes against Afghanistan where Osama Bin Laden, the prime suspect in the 11 September suicide attacks on the US, is thought to be hiding.
Funeral
Mourners, some in tears, filed past Rehavam Zeevi's coffin in front of parliament before it was taken to Mount Herzl for burial late on Thursday afternoon.
"Today we are parting from a determined and hard person whose love for the country was greater than his love of people," he said.
Rehavam Zeevi was a highly controversial politician, even by Israeli standards.
A staunch opponent of the land-for-peace deals with the Palestinians, he was shot dead outside his room in a Jerusalem hotel by two unknown gunmen early on Wednesday morning, the very day his resignation from cabinet was due to take effect.
Cabinet secretary Gideon Saar told Mr Arafat to hand over Zeevi's killers or face the consequences.
Israel, he said, would "act against the Palestinian Authority in the way currently accepted by the international community to act against a leadership that supports terror".
The cabinet also demanded that the Palestinian leader outlaw several militant groups that have carried out attacks against Israelis.
Correspondents say the cabinet's threat hints at the possibility that Israel's established policy of "targeted killings" of Palestinians allegedly involved in anti-Israel attacks could be extended to include direct attacks on Palestinian Authority officials.
The Palestinians are reported to have rejected the ultimatum and top Arafat aide Nabil Abu Rudeina accused Israel of plotting the assassination of Mr Arafat himself and other senior figures in an attempt to destroy the peace process.
Vendetta
A PFLP spokesman in Damascus named Front members arrested as Rabah Muhana, a member of the political office, central committee member Yunes al-Jarou and Hani Habib, an official in the Gaza Strip.
Kayed al-Gul, a Front official in Gaza, said: "This is bad for Palestinian national unity. It's a bad move for the Palestinian police. We ask Palestinian police to release the three leaders as soon as possible."
The PFLP said it had killed Zeevi in revenge for the killing of its leader, Abu Ali Mustafa, by Israeli forces in August.
Despite long years of bloodshed in the Arab-Israeli conflict, this is the first time ever that Palestinian militants have succeeded in assassinating an elected Israeli official.
Mr Zeevi was among the Israeli politicians most hated by Arabs because of his extreme policies which included advocating the expulsion of the Palestinian population of the West Bank and Gaza, which he viewed as land given by God to the Jews.