"President Obama has also underlined our commitment to a better future for all Palestinians ... Lasting peace is our objective and the United States will sustain an active commitment to two states living side by side in pfeace, stability and security."
Mitchell's visit to the occupied Palestinian territory on Thursday came after meetings with Ehud Olmert, the prime minister of Israel, and Simon Peres, the country's president.
The US envoy called for an opening of trade crossings into the Gaza Strip from Israel and Egypt with the involvement of the Western-backed Palestinian Authority.
"To be successful in preventing the illicit traffic of arms into Gaza, there must be a mechanism to allow the flow of legal goods, and that should be with the participation of the Palestinian Authority."
Israel maintains a tight blockade over the coastal enclave, saying it needs to prevent Hamas from acquiring arms. But Israel's grip over the territory's border crossings has starved Palestinians of crucial goods such as food, fuel and medical supplies.
The need for such goods has increased dramatically following Israel's 22-day war on Gaza, which killed more than 1,300 Palestinians and injured thousands more.
A spokesperson for Mitchell told Al Jazeera that the US envoy was not scheduled to visit Gaza, but Mitchell said on Wednesday that respective unilateral ceasefires by Israel and Hamas should be "extended and consolidated".
Nour Odeh, Al Jazeera's correspondent in Ramallah, said the issue of illegal Israeli settlements in the occupied West Bank was likely to have been on the agenda during Mitchell's talks with Palestinian leaders.
"Settlements will be on the agenda, especially knowing Mitchell's initial assessment of the grave consequences that settlement construction has on the peace process," she said.
"In his 2001 report, Mitchell said that Palestinians view settlements as the ultimate way that Israel imposes, prolongs and entrenches its occupation of the West Bank.
"When he came in 2001, there were about 200,000 Israeli settlers living in the Israeli-occupied West Bank, against international law. That number has since jumped by about 100,000 Israeli settlers."
Palestinians will tell Mitchell they want to achieve tangible results rather than commiting to a peace process they feel has failed them, Odeh said.
"That will begin by dismantling settlements, ending the occupation, taking apart those 600 Israeli checkpoints, and many other Israeli measures that undermine not only the Palestinian Authority but also the very prospect of a two-state solution."
Mitchell's meeting with Abbas came amid continuing tensions between his Fatah faction and rival Palestinian group Hamas, which has de facto control of Gaza.
Khaled Meshaal, the political leader of Hamas who is based in Damascus, on Wednesday talked about creating an alternative body to the Palestinian Legislative Organisation (PLO), which is recognised as the sole representative of the Palestinian people.
"We can announce, after the steadfastness and victory achieved in Gaza, that we will work on establishing a national platform body - an ultimate point of reference for all Palestinians, whether inside or outside - to contain all Palestinian plans, trends, and national figures will be included as well," he said.
While the prospect of a national unity government between the rival parties appears slim, a Hamas spokesman told Al Jazeera that the organisation is keen to find common ground with Fatah.
"I think we are interested in achieving national unity among the Palestinians. We don't need more division. Hamas, Fatah and other Palestinian factions have to very quickly sit around the negotiating table," Ghazi Hamad said.