US Secretary of State Condoleezza Rice came to Israel on Thursday, patted Prime Minister Ehud Olmert on the back, and left a few hours later without leaving much of a footprint. Rice, in a brief statement before meeting Foreign Minister Tzipi Livni, praised Olmert for what she said was his "very positive speech" Monday at Sde Boker, saying it represented "a hand reaching out to a Palestinian partner." Rice, who was in Jordan along with US President George W. Bush for talks with Iraqi Prime Minister Nouri al-Malki, arrived in Jerusalem from Jericho, where she met Palestinian Authority Chairman Mahmoud Abbas. She called Abbas "a man who has been committed to a peaceful resolution of the Palestinian-Israeli conflict and the establishment of two states - democratic and independent - living side-by-side in freedom." Rice said this "has been a week of progress, a week that we hope can be consolidated. The cease-fire now needs to be consolidated by action to make certain that it is enforced." The secretary of state also praised Israel for its "statement of restraint" concerning the cease-fire, "because it is of course quite fragile, but we would like to see it consolidated and then extended." Olmert's chief-of-staff Yoram Turbowicz and foreign policy adviser Shalom Turgeman will reportedly meet next week with Abbasâ€š advisers Saeb Erekat and Rafik Husseini to discuss expanding the cease-fire to include not only Gaza, but also the West Bank. Rice only informed the Prime Ministers Office and the Foreign Ministry of her intention to visit Jerusalem on Wednesday, and only met with Olmert and Livni for about 40 minutes each. It's clear, one diplomatic source said, that matters of substance cannot be discussed during such a short meeting. The main purpose of Rice's last-minute visit to Jerusalem, said a US official, was to show support for the cease-fire and Olmert's Sde Boker speech. The Prime Minister's Office issued a statement saying that Rice briefed Olmert on her meeting with Abbas, and Olmert briefed Rice on his meeting Wednesday with Egyptian Intelligence Chief Omar Suleiman regarding the cease-fire, Gilad Shalit and the arms-smuggling tunnels from Egypt. Diplomatic officials said that the tunnel issue - and not Shalit - was the focus of Olmert's talks with Suleiman, with Israel continuing to press the Egyptians to show more action and take more initiative in clamping down on the smuggling.