Mitchell's visit is being closely watched after it was delayed following an announcement by Israeli that it planned to build 1,600 settler homes in East Jerusalem, prompting Palestinians to pull out of indirect, US mediated talks.
The Israeli announcement, which was made as Joe Biden, the US vice-president, visited Israel was seen as an insult to the US and frayed Israel's usually strong ties with Washington.
The US rebuked Israel and made a series of demands, thought to include a call for an official declaration that talks with the Palestinians would address core issues such as settlements, the right of return and Jerusalem.
Binyamin Netanyahu, the Israeli prime minister, is expected to communicate the extent of Israel's agreement to Mitchell during his visit.
But Nisreen el-Shamayleh, Al Jazeera's correspondent reporting from Jerusalem, said the US envoy would probably struggle to achieve a breakthrough on the settlements issue.
"He [Mitchell] needs to convince the Israelis to stop these projects ... but I think it's going to be very difficult to convince Netanyahu to stop these projects," she said.
"Israeli officials and the Israeli government have both made it very clear that they do not consider settlements in East Jerusalem as being built on occupied land."
Netanyahu appeared to be standing firm on Israeli construction in East Jerusalem on Sunday.
The Israeli leader told his cabinet: "Our policy on Jerusalem is the same policy followed by all Israeli governments for the 42 years, and it has not changed. As far as we are concerned, building in Jerusalem is the same as building in Tel Aviv."
Israeli media said that among Netanyahu's concession would be an easing of Israel's blockade of the Gaza Strip, which is run by Hamas and which has been under a punishing siege for about three years.
The UN's Ban crossed into Gaza on Sunday, visiting the Gazan town of Khan Younis where he criticised the Israeli blockade.
"I have repeatedly made it quite clear to Israel's leaders that the Israeli policy of closure is not sustainable and that it's wrong. It causes unacceptable sufferings," Ban said.
The UN secretary-general's Gaza visit follows on from a tour of the West Bank a day earlier where he reiterated demands that Israel end settlement building in Palestinian territory.
"Let us be clear, all settlement activity is illegal anywhere in occupied territory and this must stop," Ban said, speaking at a joint news conference with Salam Fayyad, the Palestinian prime minister.
Ban emphasised the commitment of the so-called international Quartet of Middle East negotiators - comprised of the UN, the European Union, Russia and the US - to the establishment of a Palestinian state.
"The Quartet has sent a clear and strong message: we are strongly supporting your efforts to establish an independent and viable Palestinian state," Ban said.
He also met Israeli officials, including Shimon Peres, the Israeli president, as part of his trip.
But the moves on the diplomatic stage come amid violence on the ground in the West Bank.
Two Palestinians were shot dead by Israeli forces on Sunday,bringing to four the total number of Palestinians killed in the West Bank in the last two days.
|Two Palestinians were killed in the
protests in Nablus on Saturday [AFP]
On Saturday a Palestinian boy, identified as 16-year-old Muhammad Qadus, was apparently shot dead by Israeli forces while taking part in a demonstration in the city of Nablus.
Another Palestinian youth was injured in the same clash and later died of his wounds.
The Israeli military denied its soldiers had used live ammunition at the protest, saying they had used only riot control weapons such as teargas and rubber-coated bullets.
But a Palestinian doctor has said X-rays prove the military's claim was false and that the boy had been stuck by live ammunition.
The Israeli military has said it will investigate the incident.