Vice President Dick Cheney met Sunday with Israeli and Palestinian leaders here and in the West Bank city of Ramallah in what American officials described as an effort to promote the peace process.

But Israeli officials seemed more interested in seeking Mr. Cheney’s help with broader regional issues, chief among them the perceived threat from Iran, while Palestinian officials expressed deep pessimism about the peace process and prospects of success.

Welcoming Mr. Cheney at a joint news conference at the prime minister’s residence here on Saturday night, Prime Minister Ehud Olmert pointedly placed Iran before the peace process as one of “the many items on the common agenda” to be discussed.

“We are both very concerned about Iran,” Mr. Olmert said. “We are anxious to carry on the peace negotiations with the Palestinians.” He then mentioned Lebanon, Syria and the attacks on Israel from Gaza.

Although Mr. Cheney has less than 10 months left in office, an Israeli official, who spoke on condition of anonymity because he was not authorized to discuss the visit, said he was seen in Jerusalem as “a significant player” who could influence “serious issues that cannot wait.”

Before dinner with Mr. Olmert on Saturday night, Mr. Cheney offered robust support for Israel.

“America’s commitment to Israel’s security is enduring and unshakable, as is our commitment to Israel’s right to defend itself always against terrorism, rocket attacks and other threats from forces dedicated to Israel’s destruction,” Mr. Cheney said. The United States, he said, “will never pressure Israel to take steps that threaten its security.”

Mr. Cheney, who is not known to have been previously involved in the details of the peace process, sounded somewhat less committal regarding the Palestinians.

He said that “history has clearly shown” that Israelis were prepared to make sacrifices for peace when they encountered Arab partners like Anwar el-Sadat of Egypt and King Hussein of Jordan, “who accepted Israel’s permanence, and are willing and capable of delivering on their commitments.”

“I have no doubt this is equally the case with Palestinians,” he said, refraining at that point from mentioning Mahmoud Abbas, the Palestinian president, by name.

Mr. Cheney also warned against ignoring “the darkening shadows” from Gaza, which is controlled by the Islamic militant group Hamas, and from Lebanon, Syria and Iran.

Mr. Cheney’s visit to Israel and the West Bank was part of a 10-day tour of the region, with stops in Iraq, Oman, Afghanistan and Saudi Arabia, that continues Monday in Turkey.

The vice president started the day with an Easter service in the small chapel of a monastery in the United States Consulate compound in West Jerusalem. He was accompanied by members of his family and the consulate staff.

Later in the morning, he flew by helicopter to Ramallah, where he met with Mr. Abbas and Salam Fayyad, the Palestinian prime minister. According to Mr. Cheney’s spokeswoman, Lea Anne McBride, the purpose was to “reaffirm the president’s commitment to the current efforts toward the two-state solution and efforts to strengthen Palestinian institutions.”

This incarnation of the Israeli-Palestinian process began at an American-sponsored peace conference in Annapolis, Md., last November. The sides pledged to try to reach an agreement on the core issues by the end of President Bush’s term in January.

Talks have been bogged down by waves of violence in and around Gaza and by Mr. Olmert’s domestic political constraints. But American officials are eager to get the process moving again before President Bush’s next trip here, planned for May to coincide with Israel’s 60th anniversary celebrations.

In an appearance with Mr. Abbas in Ramallah, Mr. Cheney said that Palestinian statehood was long overdue but that continuing terrorism and rocket attacks could “kill the legitimate hopes and aspirations of the Palestinian people.”

Mr. Abbas said security and peace “will not be realized” if Israel continues building settlements in the West Bank and does not remove roadblocks there. The Israeli government recently announced the resumption of a long-frozen construction project in a West Bank settlement and plans for further building in areas of East Jerusalem that the Palestinians claim as part of a future state.

Saeb Erekat, a senior Palestinian negotiator, told reporters in Jerusalem last week, “It’s either settlements or peace.”

Mr. Cheney said that peacemaking also required “a determination to defeat those who are committed to violence” and deny Israel’s right to exist, meaning Hamas.

That statement seemed at odds with some recent developments in the region. Egypt has been holding separate talks with Israeli officials and representatives of Hamas in an attempt to reach an understanding for an extended period of calm, Egyptian officials and Hamas leaders have said. Those efforts have tacit American support.

Also on Sunday, representatives of Hamas and Mr. Abbas’s Fatah faction signed a document in Sana, Yemen’s capital, agreeing to use a Yemeni proposal “as a framework for the resumption of dialogue between the two movements for the return of the Palestinian situation to what it was” before June 2007. That was the month Hamas seized control of the Gaza Strip in a brief factional war in which it routed Fatah. Mr. Abbas subsequently fired the Hamas-led unity government, in which Fatah had participated, and appointed an alternative government in the West Bank.

Hamas has long declared its readiness for negotiations to restore national unity, but Fatah has so far demanded that Hamas rescind control of Gaza before talks are held.

Fatah officials said the talks should focus immediately on carrying out the Yemeni proposal, which calls for Gaza to revert to its pre-June status and for new elections to be held.