The so-called "roadmap", which was agreed by the two sides in 2003, commits Israel to stop the building settlements in the West Bank and east Jerusalem and the Palestinians to reject violence.
Saeb Erekat, the chief Palestinian negotiator, said that Abbas's government was fully prepared to abide by its side of the deal.
"We are seeking to achieve a two-state solution and President Abbas reiterated also his full commitment to all our obligations eminating from the roadmap," he said.
Al Jazeera's Nour Odeh, reporting from Ramallah, said that US officials recognised that the Palestinian government was keeping its end of the bargain.
"They have been reforming security, reformming their institutions, striving for more transparency and so on," she said.
"Now the Americans are recognising that the Israelis meet their end of the bargain, which means a freeze to settlements, a lifting of the roadblocks, stopping the building of the wall and taking several steps in occupied east Jerusalem.
Binyamin Netanyahu, Israel's prime minister, is yet to commit to working towards an independent Palestinian state.
Netanyahu has, so far, said he is only ready to hold talks with Abbas on economic, security and political issues.
Palestinians have rejected his proposed shift of focus away from territorial issues.
However, there is widespread speculation in Israel that Netanyahu could back moves to create a separate Palestinian state when he outlines his policy on relations with the Palestinians in a speech on Sunday.
Ehud Barak, the defence minister in Netanyahu's coalition government, on Wednesday urged the prime minister to accept the principle of a Palestinian state.
"The current government was formed with the commitment to respect the deals reached by preceding governments," the head of the centre-left Labour party told public radio.
"The roadmap which clearly states that the conflict must be resolved on the principle of two states for two peoples."
Netanyahu's refusal to endorse a Palestinian statehood and his defiance to US calls for an end to all settlement expansion in the West Bank and east Jerusalem have created a rift with Washington.
But Mitchell sought to ease the tensions as he met Netanyahu on Tuesday.
"We are two allies, two friends, and our commitment to Israel's security is unshakeable," he said.
"And I want you to know we come here to talk not as adversaries in disagreement but as friends in discussion.
"We recognise that the issues are complex and many. But we hope that we're going to work our way through them to achieve the objective that we share with you, and that is peace, security and prosperity throughout the region."
Mitchell later travelled to Cairo, where he is scheduled to meet with Egypt's foreign minister and intelligence chief.
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.