Palestinian leader Mahmoud Abbas has promised to put an end to "armed chaos" in the Gaza Strip, a day after the withdrawal of Israeli troops.
Abbas said Israel's Gaza pullout was not an end to the occupation
"No-one is above the law," Mr Abbas said in a televised speech.
His comments come amid mass looting in Gaza's abandoned Jewish settlements, and are seen as a warning to militants seeking to challenge his authority.
But Israeli Prime Minister Ariel Sharon said he was not surprised by the lawlessness in Gaza.
In his first comments since Monday's withdrawal, Mr Sharon said the Palestinian leadership knew they needed to re-impose order, but he said he would wait and see whether they could do so.
"I didn't think it would be any other way," he said.
"This rioting - even they understand they have to control this."
Meanwhile violence continued in the West Bank. A 19-year-old Palestinian man was shot dead by Israeli troops outside the city of Hebron, Palestinian medics said.
Mr Abbas said Israel's withdrawal should not stop at Gaza.
"Today Gaza, tomorrow the West Bank and Jerusalem," he said.
Chaotic scenes continued in Gaza on Tuesday as Palestinians picked through the rubble of former Israeli settlements.
In several abandoned settlements, Palestinian police failed to stop crowds from taking building materials and equipment left by the Israelis.
In the southern Gaza Strip, thousands of Palestinians crossed into Egypt after the border opened for the first time after the Israeli pullout.
The mass crossings have raised questions whether Egypt is be able to honour its deal with Israel and maintain security along the border, correspondents say.
They say Israel is especially concerned about possible arms smuggling to Palestinian militants in Gaza.
The Palestinian commander in southern Gaza, Jamal Kaed, said roadblocks would be set up on the border by midnight local time (2100 GMT on Tuesday).
Anyone without proper documents found on the wrong side by Wednesday evening could face arrest, he added.
Meanwhile, Palestinian Prime Minister Ahmed Qurei has been touring what was the Gush Katif bloc of settlements.
He visited a school in what used to be the Palestinian enclave of Mawassi in the settlement bloc.
Mr Qurei urged Palestinians to stop looting and start rebuilding the abandoned settlements.
"You won't profit from a pillar, plastic tubing or pieces of wood that you are taking. Protect them because they are yours," he said in Neve Dekalim.
'End of military rule'
On Monday, jubilant Palestinians took control of the Gaza Strip following the Israeli withdrawal, more than 38 years after they captured the area.
Thousands entered the former Jewish enclaves, some setting an abandoned synagogue ablaze in a settlement.
Israel declared a formal end to military rule on Sunday before its remaining 3,000 troops left.
But it retains control over the territory's air and sea space and, at least temporarily, all its borders.