He also said that the US wanted the Arab peace initiative, which demands that Israel withdraw from all the land it captured in the 1967 war, "to be part of the effort to reach this goal".
But he did not elaborate on what part the Arab initiative might play in US attempts to mediate a two-state solution between Israelis and Palestinians.
'Acts of aggression'
Fatah leaders told reporters that Friday's meeting was meant to discuss ongoing efforts to reach national reconciliation and to gauge opinion on how the peace process should move forward.
Qadura Fares, a spokesperson of the Fatah delegation, said officials told Mitchell that it would not be enough for the US to pressure the Israeli government to accept the two-state solution, which would see Israel and Palestine existing as two separate entities.
Fares said Netanyahu's government should recognise the rights of the Palestinians, stop all its illegal settlement activities and "acts of aggression against the Palestinian people".
Otherwise, he warned, the principle of "two states would fall apart and the conflict would continue on a religious basis".
"If that happens, compromises and moderate solutions would have no chance," he said.
Al Jazeera's Nour Odeh, reporting from the West Bank, said that Palestinian observers had been encouraged by Mitchell's use of the word "sovereign" to describe the future Palestinian state.
"This is perhaps the first time we hear an American official use that term to talk about a Palestinian state," she reported.
"That would basically be sovereign and independent like all other states in the international community. That is a source of encouragement for Palestinians."
But she added that while Palestinian officials had welcomed Mitchell's statements, there had been no promises of any tangible steps that the US administration planned to take in order to translate that statement into a reality.
"We've heard from the new Israeli government led by the right wing Likud party and its leader Binyamin Netanyahu what they want from the Palestinians," Odeh said.
"We've also heard them say nothing about a two-state solution, so Palestinians are still waiting to hear from the Obama administration what steps they will take. They are encouraged by the signals so far, but they want to hear more."
On Thursday, Mitchell met Binyamin Netanyahu, Israel's new prime minister, who is leading a government dominated by hawks.
Israeli officials quoted Netanyahu as telling Mitchell that his right-leaning government wanted the Palestinians to first recognise Israel as a Jewish state.
Palestinians have long rejected such explicit recognition of the Jewish nature of a state where one in five people is Arab.
Netanayahu has yet to give a commitment to restart US-backed talks with Abbas on core issues such as statehood borders and the future of Jerusalem and Palestinian refugees.