A three-year-old Palestinian girl was killed in an Israeli raid on the Gaza Strip after the fatal shooting Tuesday of an Israeli near the Gaza border, in the latest uptick in Israeli-Palestinian violence.

Cross-border exchanges between Israel and Gaza have increased in recent days, and Israel said Tuesday it held Islamist movement Hamas responsible, as rulers of the Palestinian enclave, for any fire directed from there at the Jewish state.

An Israeli unit approached on Tuesday the Lebanese-Israeli border near the town of al-Adeisseh, reported the National News Agency.

It said that the unit, comprised of two armored Hummers, approached a surveillance position adjacent to the town.

Israeli Prime Minister Benjamin Netanyahu on Monday hit out at the United States for what he described as "unacceptable" wiretapping of his predecessor Ehud Olmert, as reported in the media.

"Given the close relations between the United States and Israel, there are things we cannot do, and that is unacceptable for us," Netanyahu said at a meeting of his Likud party.

Palestinian president Mahmoud Abbas urged Christian pilgrims from around the world to visit the Holy Land to mark the visit of Pope Francis, set for 2014, in a Christmas message on Monday.

The pontiff is to make a brief visit to Israel and the Palestinian territories from May 25, his first to the Holy Land, Israeli newspaper Yediot Aharonot said last week.

Palestinian leaders have ruled out the possibility of extending peace talks with Israel beyond their nine-month timeframe, chief negotiator Saeb Erakat said on Monday.

"We turn down any extension," Erakat told the official Voice of Palestine radio station, adding that some of his recent remarks about the matter had been misinterpreted.

Israeli Mossad agents operating in Ethiopia in 1962 unwittingly trained Nelson Mandela in hand-to-hand combat, weaponry and sabotage, according to a document released by Israel's state archives.

A letter from a Mossad official to the foreign ministry, dated October 11, 1962 titled "THE BLACK PIMPERNEL" and released to the public on Sunday, recalls a conversation in which "we discussed a trainee in Ethiopia named David Mobasari, from Rhodesia".

A mortar round fired from war-torn Syria struck the Israeli-occupied Golan Heights on Monday in what was believed to be "errant fire", the army said.

No casualties or damage was reported.

A rocket fired from the Hamas-ruled Gaza Strip in the early hours of Monday hit a southern Israel community without causing damage or injuries, Israeli police said.

Bomb disposal experts found the "rocket fired from the Gaza Strip" in a community near the city of Ashkelon, according to police spokesman Micky Rosenfeld. Police said the projectile hit near a school bus stop.

An explosion aboard an empty Israeli bus near Tel Aviv on Sunday that did not kill or wound anyone was a "terrorist attack," police said.

"After examining the explosives retrieved from the scene, we have concluded that this was a terrorist attack," police spokesman Micky Rosenfeld told Agence France Presse.

A Gaza-based human rights group on Sunday expressed "deep concern" at what it called Israeli troops' use of excessive force in Friday's fatal shooting of a young Palestinian.

The Palestinian Center for Human Rights said in a statement that soldiers shot dead Odah Jihad Hamad, 27, and wounded his brother Raddad, 22, as they picked through scrap in wasteland next to the Gaza-Israel frontier at Beit Hanun in the north of the coastal strip.