"We all share an obligation to create the conditions for the prompt resumption and early conclusion of negotiations," Mitchell said before meeting Peres.
"We're now engaged in serious discussions with our Israeli and Palestinian and regional partners to support these efforts."
Before setting off for the region, Mitchell told reporters at a Palestinian donors' conference in the Norwegian capital, Oslo, that renewed talks between Israel and the Palestinians would serve "the security interests of the United States".
Al Jazeera's Jacky Rowland, reporting from Jerusalem, said: "Right at the top of George Mitchell's agenda is the issue of Israeli settlements in the West Bank."
"This is an issue that the Americans feel progress can be made on and progress must be made on, in order to create the right kind of atmosphere to push on the peace process with the Palestinians, which has been stalled for a couple of years now."
Mitchell has long advocated the need for a settlement freeze as necessary for any tangible progress on peacemaking.
"Israelis and Palestinians have a responsibility to meet their obligations under the roadmap," he said on Tuesday, referring to the 2003 agreement which requires the end of settlement construction.
But Israel, apparently unfazed, has continued 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 itn 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 Monday, Barack Obama, the US president, had a 20-minute phone call with Netanyahu.
|Mitchell is to discuss Israel's illegal settlement construction during his visit [AFP]
The White House called Monday's talks "constructive" and said Obama "reiterated the principal elements of his Cairo speech, including his commitment to Israel's security".
Netanyahu's office said that the "discussions were positive and covered a range of subjects".
Netanyahu has said he is ready to hold talks with Abbas, focusing on economic, security and political issues.
But Palestinians have rejected his proposed shift of focus away from territorial issues, whose complexity, Netanyahu has said, has frustrated US-backed attempts to reach a final peace deal.
Abbas has said renewed negotiations would be pointless unless Netanyahu first endorsed Palestinian statehood and halted the expansion of settlements in the West Bank and east Jerusalem.
Mitchell also reportedly plans to travel to Syria and Lebanon during the week, which would be his first visits there since being appointed the US envoy to the region.