UN Secretary-General Ban Ki-Moon arrived in Israel on Saturday night and said that there was "renewed determination in the Arab world to push the 2002 Saudi peace proposal." "Our challenge," he said, is "to find this potential and create an implementable process that will bring peace." "I believe this is a moment of gathering dynamism," he said. "Contacts between Israeli and Palestinian leaders have resumed, the Quartet has become more active and hopes to meet soon in the region itself... and there is a renewed determination in the Arab world to reinvigorate the 2002 peace initiative. Our challenge is to weave these strands of potential into a fabric of tangible progress." Ban's comments dovetailed with remarks that US Secretary of State Condoleezza Rice made in Washington Friday before embarking on her own Mideast tour. Referring to the upcoming Arab League summit in Riyadh that is expected to recommit itself in some form to the land-and-refugees-for peace Arab Peace Initiative of 2002, Rice said she hoped that this initiative would not be presented as an all-or-nothing deal, but as the basis of negotiations with Israel. Rice denied reports that the US, along with Israel, was asking for the Arabs to drop the clause in the initiative calling for the right of return for Palestinians and their descendants to Israel. "I have not asked them, as some have reported, to change the initiative. I think that's not appropriate. It's their initiative," she said. "But I would hope that that initiative would be offered again and offered in a way that suggests that there might be active follow-up to the initiative, not just to say here's an initiative. But to at least begin to discuss and think about how it might be actively followed up so that it becomes a part of supporting an end to the Palestinian-Israeli conflict now." Ban is expected to meet with Rice on Sunday in Jerusalem, shortly after the US Secretary of State's arrival from Egypt. He will attend the Arab League summit in Riyadh on Wednesday. Ban, who was met at the airport by Defense Minister Amir Peretz, is scheduled to hold talks Sunday with Palestinian Authority Chairman Mahmoud Abbas and other non-Hamas members of the new PA government in Ramallah. "The United Nations has had crucial political and operational roles in the Middle East for more than 60 years. We were there at Israel's creation and I would dearly wish to be there again when a comprehensive solution to the conflict is achieved," Ban said before meeting Peretz. Peretz urged the UN chief to "do everything" possible to win the release of the two soldiers, Ehud Goldwasser and Eldad Regev, captured by Hizbullah last July. "This is an unequivocal demand by the state of Israel," Peretz said. "We see it as the key to continuing the precise implementation of Resolution 1701." Ban is expected to meet PA Foreign Minister Ziad Abu Amr, an independent. On Monday he will meet Prime Minister Ehud Olmert, as well as Foreign Minister Tzipi Livni and Vice Premier Shimon Peres. Israeli officials said there was a full agenda to discuss with Ban, including the Arab peace initiative, the Palestinians, Iran, and the situation in Lebanon. Ban, who visited here as South Korea's foreign minister in 2005 but who is making his first visit as the UN secretary-general, arrived from Cairo where he held talks with Egyptian President Hosni Mubarak. Ban urged the new PA government to live up to the international community's three criteria - recognize Israel, renounce violence and accept previous agreements. "We expect that the national unity government will meet the expectations of the international community for peace and security in the region," Ban said. He said he discussed the need "to encourage this ongoing peace process" with Mubarak. Rice, meanwhile, was also in Egypt on Saturday and held talks with the foreign ministers of Egypt, Jordan, Saudi Arabia and the United Arab Emirates - the so-called Arab Quartet. Besides foreign ministers from those nations, Rice was meeting separately with intelligence and security chiefs. She held a similar discussion on Jordan last month following a trilateral meeting here with Olmert and Abbas that focused on how to deal with Hamas. While her visit here now, the second in just over a month, is considered partly as an attempt to show the Arab states that the US is committed to pushing the Israeli-Palestinian diplomatic track forward, she has been arguing to Arab allies that they should consider parallel overtures that could strengthen her hand. "You need the energy and the help of moving forward on the Arab-Israeli side not at the end of the process but earlier," Rice said Friday in Washington. According to Israeli officials, the US has begun talking recently of the need for the Arab states to take some steps toward normalization of ties with Israel before a final Palestinian-Israeli deal is struck, in the belief that this would make striking that deal easier. "It is absolutely the case that I see the Israeli-Palestinian issue as having to be augmented by - assisted by and, in fact, you could even say, it's embedded in a broader Arab-Israeli reconciliation," Rice said in Washington. Rice also made clear that despite the cabinet's recent decision that Israel would limit its talks with Abbas to security and humanitarian issues, and not to "political horizon" topics, she was set on discussing the larger "political horizon" issues during her separate meetings with Olmert and Abbas. "We're going to discuss the political horizon," Rice said, adding that this time she would do this separately with both leaders. "I'm going to try as much as I can to enter into discussions that are confidential with them about these complicated issues," she said. Rice is scheduled to meet with Abbas Sunday, and then with Olmert Monday morning. She is then expected to travel to Jordan Monday for a meeting with King Abdullah and another meeting with Abbas, and then come back to Israel for another meeting with Olmert, as well as separate meetings with Livni and Peretz. She is expected to fly back to Washington on Tuesday. In addition to Ban, Swedish Foreign Minister Carl Bildt arrived in Israel Saturday night and was scheduled to meet Livni Sunday. He is also scheduled to meet, in line with EU policy, non-Hamas Palestinian officials. AP contributed to this report.