VIDEO - Secretary of State Condoleezza Rice will ask the Bush administration's Arab allies for help this week to shore up Palestinian President Mahmoud Abbas at the expense of the Hamas radicals who control part of the Palestinian government. The top US diplomat is also looking for ways to strengthen Lebanon's democratic government following Israel's 34-day war with Hizbullah militants in southern Lebanon. She has diplomatic meetings in Saudi Arabia and Egypt before she travels to Israel and the West Bank. "I think that the Saudis have demonstrated their desire to help, for instance, Abu Mazen," Rice said, using Abbas' nom du guerre. "I think we can talk about how we might do more to help Abu Mazen, and particularly to help Lebanon." Rice was meeting Tuesday with eight Arab allies in Cairo in hopes of reviving the moribund Arab-Israeli peace process and making headway on other regional issues. During that session, the ministers of the six-nation Gulf Cooperation Council and Egypt and Jordan are expected to coordinate efforts to buttress Abbas' stature and stem Iran's growing influence. The trip comes as Arab countries have in recent weeks halted dealings with Hamas. They want it to join a unity government that supports a 2002 Arab League plan that would offer peace to Israel in exchange for land and they've even started funneling aid through Abbas, Arab diplomats say. Hamas trounced Abbas' secular political movement in January elections but has been unable to govern effectively because of the power split with Abbas and a cutoff of Western and most other international aid after the Hamas victory. The United States and Israel consider Hamas a terror group and refuse to deal with it unless it renounces violence, recognizes Israel and agrees to abide by agreements the struck by the previous Palestinian leadership. Abbas was elected separately and retains his position, but the stalemate has hamstrung him as well. Rice to discuss Iran nukes The Bush administration and Israel are increasingly convinced Hamas will crumble, and look to Abbas to capitalize. Rice may ask other countries to do more to bolster Abbas' security forces, and she hopes to breathe life into stalled agreements and talks that would help Palestinians move more freely across their borders with Israel. During a visit by Abbas to Jordan on Monday, Jordan's prime minister urged the world to financially support the Palestinian Authority so it can pay the salaries of government employees. Paying the salaries, now in arrears for six months or more, would probably be the single most important feather in Abbas' cap at home. Egypt, a longtime mediator among Palestinian factions and between Israel and the Palestinians, appears to be losing its patience with Hamas. Last week, Egypt's powerful chief of intelligence Omar Suleiman demanded of Hamas the immediate release of Israeli Cpl. Gilad Shalit. Militants close to Hamas captured the soldier in June, triggering Israeli military retaliation. Suleiman has been working for months on a prisoner swap deal. Iran's nuclear ambitions will also be part of Rice's discussions, as an unofficial deadline passes this week for Iran to heed a UN Security Council demand to shelve disputed nuclear activities. In a briefing with reporters en route to the Mideast, Rice said Sunday she may close her trip Friday with a meeting of world powers in Europe to look at what to do next. The United States wants to press for UN Security Council sanctions, but it is not clear she has full support from other permanent members of the council.