Israeli soldiers shot and "hit" two Palestinians as they tried to cut through the security fence separating Israel from the Gaza Strip on Monday, an Israeli army spokesman said.

But it was not immediately clear if the Palestinians were wounded or killed in the shooting near the Beit Hanun area of the Hamas-ruled Gaza Strip, the Israeli official added.

Justice Minister Tzipi Livni, who heads the Israeli team in peace talks with the Palestinians, said late Saturday in Washington that a two-state solution was in her country's best interest.

"The only way to keep Israeli values as a democratic state is by adopting the idea of two states for two people," one for Israelis and the other for Palestinians, Livni said at a conference held by J Street, a leftist pro-Israel lobbying group.

A rocket fired from the Gaza Strip hit southern Israel overnight, the army said on Saturday, but no casualties or damage were reported.

A tweet from the official military account said the rocket struck open ground near the port city of Ashkelon just northeast of the Islamist Hamas-ruled Palestinian enclave.

Israeli police arrested nine Palestinians and tried to disperse stone-throwing youths outside Jerusalem's Old City on Friday, a spokeswoman said.

Palestinians threw stones at policemen at Damascus Gate in Arab east Jerusalem, lightly injuring one, in ongoing small-scale clashes that followed Friday prayers, Luba Samri said in a statement.

Israel has announced that it is easing some restrictions on the impoverished Gaza Strip and West Bank as it negotiates a final peace deal with the Palestinians.

Israeli minister of international relations Yuval Steinitz said Wednesday that 5,000 new work permits were being issued for Palestinians to work in Israel, the opening hours of the key Allenby Bridge crossing would be extended, and new imports of some building materials would be allowed into Gaza.

The United States is planning to step up efforts to help reach an elusive Middle East peace deal, having set an ambitious goal of sealing an agreement within nine months.

U.S. Secretary of State John Kerry revealed for the first time Wednesday that Israeli and Palestinian negotiators have now met directly seven times since the peace talks were relaunched in late July.

Continued control of the Gaza Strip by Islamist movement Hamas is in Israel's security interests, the Israeli army's top commander for the region said on Tuesday.

It was the first time a senior commander had publicly stated an Israeli interest in continued control of the territory by a group with which it fought a deadly eight-day conflict just last November.

U.N. Secretary-General Ban Ki-moon on Tuesday called on states to stop sending weapons to the Syria conflict as the United States and Russia wrangled over destroying Syria's chemical weapons.

"I appeal to all states to stop fueling the bloodshed and to end the arms flows to all parties," Ban said as he opened the annual U.N. General Assembly.

An Israeli soldier died after being hit by gunfire in the southern West Bank city of Hebron on Sunday, the Israeli army said.

"An IDF (Israel Defense Forces) soldier was killed from gunfire fired this evening at an army force in Hebron," a statement from the military read.

Israel on Sunday answered EU anger over the confiscation of humanitarian aid for Palestinians with accusations diplomats at the scene defied a court order and one struck a policeman.

"Diplomats are sent by their governments to be a bridge and not act as provocateurs," the foreign ministry said in a statement.