Secretary of State Condoleezza Rice said Tuesday the Hamas government cannot govern in the Palestinian territories and she urged the Islamic militants to moderate and cooperate with the secular president.

Rice also said the world's credibility is on the line in the nuclear standoff with Iran as U.N. diplomats declared last-ditch talks with Tehran a likely failure. She said the nations that could impose sanctions are unified, despite Russia's public misgivings Tuesday.

"The international community is running out of time because soon its own credibility in terms of enforcing its own resolutions will be a matter of question," Rice said midway through a Middle East tour.

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Although she got a polite hearing from the United States' two most powerful friends in the Arab world, Rice also got a lecture. Saudi Arabia and Egypt both told Rice on Tuesday that the Middle East's many volatile conflicts are hinged to Israel's long conflict with the Palestinians.

Arab nations, including the few moderate states that are key to U.S. goals in Iraq, Iran and Lebanon, view improving the Palestinians' lot as essential. They argue that the festering grievances of the stateless Palestinians feed unrest and radicalism elsewhere.

"The issue is how to make peace, and in order to make peace you have to identify the problem," Egyptian Foreign Minister Ahmed Aboul Gheit said during a sometimes strained news conference with Rice.

"We think and we claim and we keep telling everybody that it is the Palestinian problem, and the lack of a settlement for the Palestinians. The Palestinian problem is the scourge of this region," Gheit said.

Saudi Foreign Minister Saud al-Faisal likened the nearly 60-year-old conflict to a disease that weakens the body and invites further infection.

"Whenever there is an answer to question in justice and the rights of people are not responded to, it's a breeding ground for extremism," Saud said with Rice by his side in Jedda, Saudi Arabia. "There is a very short step from extremism to terrorism. And ever since the problem arose of Palestinian-Israeli conflict, the region has been destabilized."

Rice is in the Middle East this week seeking ways to strengthen Palestinian President Mahmoud Abbas in his standoff with Hamas radicals who control part of the Palestinian government. Rice was to meet with Abbas on Wednesday.

Rice's talks in Ramallah will be the administration's third meeting in less than three weeks with Abbas, whom President Bush called a "man of courage" for trying to revive Mideast peace talks.

Rice wants Saudi Arabia and Egypt to put greater diplomatic muscle behind the secular Palestinian president in his standoff with Hamas militants, and to bolster moderate secular governments in Lebanon and Iraq.

Rice met in Cairo with diplomats from Egypt and seven other Arab allies 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 gave broad support to Abbas, Rice said.

Her first appointment in Egypt was with the country's intelligence chief, seen as key to ongoing efforts to release an Israeli soldier captured in June by militants close to Hamas.

The top aide to Egyptian President Hosni Mubarak last week demanded that Hamas release the soldier, Cpl. Gilad Shalit, immediately.

Egypt is a longtime mediator among Palestinian factions and between Israel and the Palestinians, and its exasperation with Hamas may signal a turning point.

Israel wants to reopen dialogue with Abbas and work with him to establish a Palestinian state. But Abbas has been in a weakened position since January when Hamas, which seeks the destruction of Israel, won the Palestinian elections.

Abbas retains his position as president but is caught between Hamas and the West, which considers Hamas a terrorist group and refuses to underwrite it with vital international aid. Abbas has tried to persuade Hamas leaders to moderate their anti-Israel policies and join with his Fatah Party in a coalition government, but the U.S. and Israel are leery of the plan.

"Clearly, they cannot govern in a circumstance in which they cannot represent a responsible government before the international system," Rice said in Saudi Arabia. "I would hope that they would take up what I understand to have been many overtures" by Abbas.

The Bush administration and Israel are increasingly convinced Hamas eventually will crumble, and they look to Abbas to capitalize.

Complete coverage is available in FOXNews.com's Mideast Center.