In the most public rift between the US and Israel in a decade, Barack Obama, the US president, has piled on the pressure on Netanyahu to stop settlement expansion and endorse a Palestinian state, neither of which the Israeli leader has done.
Netanyahu has said he will outline his policy on relations with the Palestinians in a speech on Sunday.
Netanyahu has said so far said he is ready to hold talks with Abbas, but only focus on economic, security and political issues.
Palestinians have rejected his proposed shift of focus away from territorial issues.
Al Jazeera's Nour Odeh, reporting from Ramallah, said that there was some concern among Palestinian officials that Mitchell would push for peace talks even if Israel refused to back down on settlement expansion and a Palestinian state.
The Palestinians say such talks would not achieve anything positive, our correspondent reported.
Mitchell, who also met Ehud Barak, Israel's defence minister, Avigdor Lieberman, the foreign minister, and Shimon Peres, the president, is expected to hold talks with Mahmoud Abbas, the Palestinian president, in the occupied West Bank on Wednesday.
The US envoy has long advocated the need for a settlement freeze as necessary for any tangible progress in peacemaking.
|Israeli settlements in the occupied West Bank are illegal under international law [EPA]
Marwan Bishara, Al Jazeera's senior political analyst, said freezing the settlements would only freeze the problem between the Israelis and Palestinians, not resolve it.
"It will only stop the conflict from escalating," he said, adding that it remained to be seen whether Israel would listen to Obama since successive US leaders had made similar demands of Israeli but to no avail.
He pointed out, however, that Obama had called the settlements "illegitimate", not just illegal, and that could mean the US taking a tougher position on the issue.
Despite the pressure from Washington, Israel remains apparently unfazed, continuing to build or expand settlements that are considered illegal internationally, arguing that so-called natural expansion cannot be stopped.
Settlement construction has doubled since Israel recommitted to halting it at the Annapolis conference 18 months ago and there are plans for 75,000 new housing units, one-third of which have already been approved.
Half a million Jews already live in settlement blocks in the West Bank and East Jerusalem.
On his fourth visit to the region, Mitchell is also expected to hold meetings in Beirut, the Lebanese capital, on Thursday and Damascus, the Syrian capital, on Friday and Saturday.