Mr Abbas's office said the talks were "positive"
The US is seeking an "early conclusion" of peace talks leading to Palestinian statehood, its special Mid-East envoy said after talks in Ramallah.
Former Senator George Mitchell was speaking to reporters after meeting Palestinian Authority President Mahmoud Abbas in the West Bank town.
The US is experiencing unusual tension in relations with Israel over its opposition to Palestinian independence.
He said meeting both sides' aspirations was the "only viable solution".
"The president of the United States and Secretary of State have made our policy clear - the only viable resolution to this conflict is for the aspirations of both sides to be met through two states," Mr Mitchell said in a prepared statement.
"As President [Barack] Obama said last week, America will not turn our back on the legitimate Palestinian aspiration for dignity, opportunity and a state of their own," he said.
The BBC's Paul Wood in Jerusalem says the Palestinian leadership is feeling a sense of diplomatic momentum, while Israel's prime minister,
is now under enormous pressure.
On Monday Mr Mitchell met Mr Netanyahu in Jerusalem, where he also
called for a two-state solution
- which the Israeli leader has refused to endorse.
Mr Netanyahu is scheduled to give a major foreign-policy speech on Sunday.
Mr Mitchell is visiting in the wake of US President Barack Obama's
keynote speech in Cairo
Mr Obama called for a "new beginning" between Muslims and the US and described the Palestinians' situation in exile in neighbouring countries and under Israeli occupation as "intolerable".
Amid speculation that Prime Minister Benjamin Netanyahu may spell out his government's view on a two-state solution, centre-left Israeli Defence Minister
warned that failure to reach such an agreement would result either in a state that was no longer Jewish, or an "apartheid regime".
Benjamin Netanyahu is understood to favour Palestinian self-rule in an entity which has no army and does not control its own airspace or borders.
President Obama seems to hope he can achieve a historic Middle East settlement within his first term and this ambitious goal puts him on a collision course with Mr Netanyahu's government, our correspondent says.
The immediate clash, however, will come over the issue of Jewish settlements built on land occupied by Israel in the 1967 war.
Mr Obama has said more clearly than any US president for a long time that settlement building must stop, while Mr Netanyahu is sticking to the established Israeli formula that there should be "natural growth" in existing settlements.
After his talks with Mr Netanyahu, Mr Mitchell stressed the "unshakeable" US commitment to Israeli security, amid Israeli fears over increased US pressure.
"We come here to talk not as adversaries in disagreement but as friends in discussion," he said.
After Israel and the West Bank, the US envoy is to head to Lebanon before visiting Syria on Friday and Saturday as part of increased diplomatic engagement by the Obama government with Damascus.
The Palestinian Authority says it will not return to negotiations with Israel unless it freezes
Jewish settlement activity in the West Bank
and openly backs a two-state solution to the Israeli-Palestinian conflict.