Rice met Palestinian Prime Minister Ahmed Qureia, together with several Palestinian cabinet ministers on Saturday, at the start of a day-long series of talks.
Later she was to meet President Mahmoud Abbas and Palestinian Interior Minister Nasser Yousef, who is responsible for the Palestinian security forces, amid signs the Palestinians were buckling under heavy Israeli and US pressure to clamp down on resistance groups such as Hamas and the Islamic Jihad.
"Rice demanded more Palestinian efforts to consolidate the truce," said Palestinian Planning Minister Ghassan Khatib, who attended the meeting. Israel and the Palestinians declared an end to the more-than four years of violence at a February summit in Egypt.
Earlier, Rice welcomed the actions of the Palestinian police.
"The Palestinians have begun to act," she said. "I would just encourage them in that work because I am quite certain that Palestinian mothers and fathers and grandparents want a world in which their children can live in peace and prosperity just as Israeli parents and grandparents want the same for their children."
Palestinian policemen's efforts
have been praised by Rice
Palestinian sources said the talks would centre on encouraging the PA to coordinate the withdrawal with Israel and prevent the occurrence of a "security vacuum" in Gaza after the Israeli withdrawal.
Assurance from Israel
Abbas is expected to tell Rice that the PA will do its part, but needed Israel to hold its end of the agreement as well.
"I will tell her we need answers from the Israelis. Is Gaza going to be turned into a large prison? The Israelis are not cooperating," Abbas told reporters in Ram Allah on Friday.
"We need information on how the disengagement will take place, when and where will it begin, what is the fate of the border crossings, what is the fate of the Palestinian airport? We are not getting any answers."
PA officials told Aljazeera.net they would press Rice to ensure that Israel took concrete steps towards ending its occupation of the West Bank.
"We will tell Rice that we consider the withdrawal from the Gaza Strip is only the beginning toward ending the occupation," said Majdi al-Khalidi, a spokesman for the Palestinian Foreign Ministry.
Al-Khalidi pointed out that the Palestinians welcomed Israeli withdrawal from any part of the occupied territories.
Abbas: more information is
needed on the Gaza pull out plan
However, he hinted that many Palestinians were concerned that Israel would utilise the Gaza withdrawal in order to tighten its grip on the West Bank where 95% of Jewish settlers live in illegal settlements.
Last year the International Court of Justice (ICJ) at The Hague, issued an advisory ruling judging that all Israeli colonies in the West Bank, east Jerusalem and the Gaza Strip were illegal.
Israel rejected the ICJ ruling, arguing that the territories were "disputed" rather than "occupied" and that the issue should be settled in bilateral negotiations with the Palestinians.
Several Palestinian commentators and leaders have warned that a fresh wave of violence and bloodshed is inevitable unless Israel terminates its unilateral measures in the West Bank, especially the construction of the separation wall around Jerusalem as well as the expansion of Jewish settlements.
On Friday, Rice met Israeli Prime Minister Ariel Sharon at his ranch in the Negev desert.
Rice showed her support for Sharon who is facing a strong challenge from powerful messianic Jewish groups opposed to the Israeli withdrawal from Gaza.
In Israel Rice (R) confirmed her
support for Ariel Sharon (L)
Government spokesman Raanan Gissin said the hour-and-a-half meeting between Sharon and Rice was "very friendly and frank," and focused on the upcoming Israeli withdrawal from Gaza.
"The main focus was to give unequivocal support to Sharon to implement disengagement and to express the full admiration and backing of the United States," Gissin said.
Rice told Sharon and other Israeli officials, before paying a short unscheduled visited to Beirut, that the US would seek to convene a Middle East conference aimed at encouraging Arab, especially Gulf states, to normalise relations with Israel.
Rice was to meet Israeli Defence Minister Shaul Mofaz later on Saturday.
Although Rice repeatedly has said the United States will take a back seat as the Israelis and Palestinians work out their differences, her trip was seen as a sign that she planned to keep up the pressure for progress.
The hastily planned trip was Rice's third to Jerusalem and the West Bank since she took over at the State Department in January.