VIDEO - During Condoleezza Rice's meeting with Prime Minister Ehud Olmert Thursday, the US Secretary of State said she appreciated his recent speech in the Negev and pointed out that this move could contribute to calming the situation and promoting the peace process in the area. Rice updated Olmert on her meeting with Palestinian President Mahmoud Abbas, while Olmert updated Rice on his meeting with Egyptian Intelligence Chief Omar Suleiman regarding the ceasefire, smugglings across the border, and continued efforts to release Gilad Shalit. The two also discussed the Iranian issue. Rice and Livni meeting, a reportedly warm and optimistic atmosphere Israeli participants in the meeting include Dr. Yoram Turbovitch, Maj. Gen. Gadi Shamni, senior aides Shalom Turgeman and Assaf Shariv. American participants include Ambassador Dick Jones, David Welsh and Elliot Abrams. After completing her meeting with PM Olmert the Secretary met with Israeli Foreign Affairs Minister Tzipi Livni. Rice opened her statements by saying that progress had been achieved this week on there Israeli-Palestinian issue, she also said that she appreciated the restraint shown by the Israeli government. Rice called Olmert's speech earlier this week "positive", saying it reached out to the Palestinian side. The Secretary also spoke of her meeting earlier in the day with Palestinian President Mahmoud Abbas, calling Abbas a man who supports resolving the conflict peacefully. Olmert and Rice meet on Thursday (Photo: GPO) Livni also spoke before the meeting, addressing the events of the past week. She said that she aspires to implement the ceasefire and that the PM's speech in Sde Boker was an important one that sent a message to the Palestinian Authority. Livni thanked the United States and Secretary Rice both for their firm policies against terrorism and for sending an encouraging message to moderates. Rice met Thursday morning with President Abbas in Jericho, the two also held a joint press conference there. Abbas told reporters that efforts to establish a Palestinian unity government had hit a "dead-end." During their meeting Abbas proposed a return to talks with Israel to find a solution for the establishment of a Palestinian state alongside Israel in accordance with President George Bush's initiative. Abbas suggested that negotiations deal separately with solving day-to-day matters and the larger scale political ones. Abbas emphasized the need to improve the lives of the Palestinian population because the current situation is leading to despair. "Despair leads to depression," said Abbas, "and depression leads to extremism."