They also come after Wednesday's announcement by Ehud Olmert, the Israeli prime minister, that he would not run in his Kadima party's leadership elections in September following corruption scandals.
Erekat said that there were still hopes an agreement could be forged "before the end of the year".
Rice told reporters after the talks: "The issues are difficult and they have always been difficult, there is nothing surprising in that, but ... the goal remains the same."
Qurei and Livni have been meeting at least once a week since the Israelis and Palestinians committed to attempting to reach a comprehensive deal by the end of 2008.
However analysts say that with turmoil among Israel's leadership, US presidential elections in November and continued unrest between the Palestinian Hamas and Fatah factions, it remains unclear how much can be achieved.
Sean McCormack, the US state department spokesman, also said on Wednesday following Olmert's announcement that all parties were "going to keep moving forward" and that the administration would work with all "responsible" Israeli leaders.
"The fact of the matter is, if you wait for the perfect moment to try to help bring the two parties together in a final agreement, you're going to be waiting forever," he said.
The Israeli prime minister suggested earlier this week that there was little chance of reaching the end of the year deadline as it would be impossible to agree on the status of Jerusalem - parts of which Palestinians claim as the capital of any future Palestinian state.
He had said efforts to reach agreement over borders and refugees could be bridged.
Qurei had said on Tuesday after separate talks with Rice at the US state department that there would be "no agreement" without Jerusalem.
Both sides committed to forging a comprehensive deal by the end of 2008 during talks in Annapolis, Maryland, in November last year.
Rice is also expected to travel to the Middle East soon in a bid to speed up efforts on the talks.
Reports say the US secretary of state is keen to get both sides to agree on a document of understanding on key issues ahead of the UN General Assembly session in September.
McCormack would not confirm the reports, AFP said.