CAIRO, Egypt — Secretary of State Rice appealed yesterday for an end to fighting among Palestinian Arab factions and said she is looking for ways to strengthen the Palestinian president, Mahmoud Abbas, in his standoff with Hamas radicals who control part of the Palestinian Arab government.

“Innocent Palestinians are caught in the crossfire, and we call on all parties to stop,” Ms. Rice said of the worst violence among Palestinian Arabs since March. “The Palestinians deserve calm.”

New gunbattles erupted Monday night between Fatah gunmen and Hamas militiamen in the southern Gaza town of Rafah, killing two people and wounding 14 — a day after a deadly explosion of internal violence paralyzed the Gaza Strip. Ms. Rice spoke during a news conference in Jeddah, Saudi Arabia, with her Saudi counterpart as she began a Middle East tour intended to shore up Mr. Abbas, as well as the secular Arab governments in Lebanon and Iraq.

She later flew to the Egyptian capital, where she held a private meeting with the country’s chief of intelligence, Omar Suleiman. She was also meeting with the Egyptian foreign minister, Ahmed Aboul Gheit.

Mr. Aboul Gheit told reporters that they discussed how America could contribute to efforts to urge the U.N. Security Council and the Middle East mediators group, the Quartet, to move the peace negotiations forward and broker a meeting between Prime Minister Olmert of Israel and Mr. Abbas.

While in Cairo, Ms. Rice planned to meet with eight Arab allies in hopes of reviving the peace talks 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 Mr. Abbas’s stature and stem Iran’s growing influence. Hamas’s chief in Damascus, Khaled Meshaal, called three Arab leaders Monday to fill them in on the efforts to contain the Palestinian Arab infighting. He spoke to leaders of Qatar, Yemen, and Sudan and urged Arab countries to live up to their responsibilities in lifting the siege on the Palestinian Arabs, Hamas’s official Web site said. This was ahead of Ms. Rice’s meeting with Arab foreign ministers.

Ms. Rice’s trip came 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 Mr. Abbas, Arab diplomats have said.

A longtime mediator among Palestinian Arab factions and between Israel and the Palestinian Arabs, Egypt appears to be losing its patience with Hamas.

Last week, Egypt’s powerful chief of intelligence, Mr. Suleiman, demanded that Hamas release Corporal Gilad Shalit of Israel. Militants close to Hamas captured the soldier in June, triggering Israeli military retaliation. Mr. Suleiman has been working for months on a prisoner swap deal. The Iranian nuclear crisis is also part of Ms. Rice’s agenda this week, as an unofficial deadline passes for Iran to heed a U.N. demand to at least temporarily stop its enrichment of uranium. The enriched uranium can be used either to build nuclear weapons, as America claims Iran seeks to do, or to fuel nuclear energy reactors, as Iran says it intends.

Ms. Rice said she hopes Iran may still accept a bargain that would provide economic incentives for a rollback of the nuclear enrichment program.