Jerusalem/Gaza, Sep 16 (DPA) Israelis and Palestinians have begun tackling the "most difficult" corissues of their mutual conflict, the US said Wednesday, but the second round of direct peace negotiations was overshadowed by a surge of violence in Gaza.

Briefing reporters at the end of a more than two-hour parley between Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas in Jerusalem, US envoy George Mitchell said the new negotiations had moved "very quickly" and "vigorously" to serious and substantial questions at the centre of the conflict.

"We recognise that there are serious issues and challenges that are highly sensitive for both leaders," said Mitchell. "To me it is extremely impressive to see them both so engaged.

"It is an indicator ... that peace is possible and that it is possible to conclude an agreement," he said.

The US envoy added the two parties had agreed their negotiators would continue discussions next week. They would then decide when the next Abbas-Netanyahu summit would take place.

The day of talks in Jerusalem followed a day of sessions in the Egyptian Red Sea resort of Sharm el-Sheikh Tuesday, in which Abbas and Netanyahu also held two face-to-face meetings.

Their parley in Jerusalem was the first time in two years that Abbas visited the Israeli prime minister's residence in Jerusalem. He had been reluctant to enter into direct negotiations with the nationalist Israeli leader, and the current talks, launched in a first round in Washington early this month, come more than a year after the right-leaning Netanyahu government took office.

Abbas wrote in the guest book that he returned to the prime minister's residence after a long absence to continue the negotiations out of "hope" for an eternal peace in the entire region.

But a surge in rocket and mortar fire and an Israeli retaliatory airstrike on a smuggling tunnel in southern Gaza that killed one Palestinian and injured three others overshadowed the talks.

The airstrike in the southern Gaza town of Rafah came after Gaza militants fired at least 10 projectiles at Israel Wednesday - the largest number of projectiles fired from Gaza in a single day since March 2009.

They included a Russian-type Grad rocket, the first to hit north of the southern Israeli coastal city of Ashkelon since the Gaza war of the winter of 2008-2009, Israeli Channel 2 television reported, as well as two phosphorous bombs.

The Israeli military confirmed the strike, noting in a statement that the tunnel was used to smuggle militants into the coastal strip "so that they could execute attacks against Israeli civilians".

A senior Israeli military officer, meanwhile, warned that Israel expects militants to launch more rockets and mortars at the Jewish state during the ongoing peace talks.

The officer, who spoke to journalists on condition of anonymity, said militants in Gaza had in the past few days stepped up their activity, including the planting of explosives near the border with Israel as well as sniper fire at soldiers patrolling the security fence along it.

Since Sunday, four Palestinians have been killed and at least five injured, one critically, in Israeli retaliatory airstrikes and artillery shelling.

Gunmen of the radical Islamist Hamas movement ruling Gaza killed four Israelis, and wounded two others in two separate attack two weeks ago, as Israelis and Palestinians were meeting in Washington to relaunch the long-awaited direct negotiations.

US Secretary of State Hillary Rodham Clinton, meeting Israeli President Shimon Peres earlier Wednesday, urged Israelis and Palestinians to have faith in the new peace negotiations, even though she said she understood the widespread "scepticism, doubt and disappointments" felt by both sides.

"I'm well aware of the obstacles that stand in the way of peace," she said, but added the status quo was unsustainable and the only path to ensure Israel's future as a Jewish and democratic state was a comprehensive regional peace agreement.

After meeting Peres, the secretary of state also held talks with Palestinian Prime Minister Salam Fayyad in Jerusalem. She met Netanyahu in the late afternoon, before she and Mitchell joined Abbas and Netanyahu in their direct parley.

Clinton was scheduled to make the short journey from Jerusalem to the West Bank city of Ramallah Thursday for another private talk with Abbas.

On Wednesday, she did not address the contentious issue of Israel's partial freeze of construction in the occupied West Bank, which is due to expire Sep 26 and threatens to jeopardise the nascent direct talks. But in Sharm el-Sheikh Tuesday, she insisted Israel should not resume building in Jewish settlements in the West Bank.

Israeli media reported Wednesday however that Washington was trying to work out a compromise to the Palestinian demand for a full freeze, under which Israel could build up to 2,000 housing units a year in 1.9 percent of the West Bank, which Abbas agreed to give up in a land swap deal in previous negotiations with former Israeli premier Ehud Olmert.