WASHINGTON — High gasoline prices and prospects for an Israeli-Palestinian peace deal headline Vice President Cheney’s trip to the Mideast, but fears about Iran’s rising influence will be a key topic of his private talks at each stop.

Mr. Cheney left today on a 10-day trip that includes visits to Oman, Saudi Arabia, Israel, the Palestinian Arab territories, and Turkey. His trip coincides with the fifth anniversary of the American-led invasion of Iraq, which has tainted the American image in the Middle East and changed the balance of power in the region.

Mr. Cheney is the latest top American official to go the Middle East to coax Israel and moderate Palestinian Arab leaders to move forward on a peace deal. President Bush went to Israel and the West Bank in January. Secretary of State Rice just got back from a troubleshooting mission there, and mr. Bush is to return in May. Senator McCain, the soon-to-be Republican presidential nominee, and other lawmakers are visiting Israel this week.

Mr. Bush, who relaunched formal peace talks last fall at a conference in Annapolis, Md., has turned a Middle East peace deal into a signature foreign policy goal for his remaining months in office. But violence in the Gaza Strip and southern Israel has hampered talks between Prime Minister Olmert of Israel and the president of the Palestinian Authority, Mahmoud Abbas.

Mr. Bush has made clear that he wants Mr. Cheney to push both men to honor their obligations under the American-backed road map, which calls for the Palestinian Arabs to disarm militants and for Israel to halt settlement construction. Last week, the Bush administration said Israel’s recently announced plan to build hundreds of new Jewish homes in disputed areas of the West Bank and east Jerusalem was not helping move the peace plan along.

On Iraq, Mr. Cheney will highlight progress made since the president dispatched 30,000 additional American troops there last summer to help secure the nation and give political leaders a chance to reconcile their differences.

America wants Saudi Arabia and other Arab nations to establish a diplomatic presence in Baghdad to help anchor the Iraqi government in the Arab world. In the meantime, the Bush administration feels there is no reason why trade, culture, economic, and foreign ministers from the Arab world shouldn’t go to Iraq and engage the new Iraqi government as they would others in the region.

It’s unclear what Mr. Cheney will seek from Saudi Arabia about easing pressure on oil prices. When Mr. Bush visited Saudi Arabia’s King Abdullah in January, he urged the 13-nation Organization of Petroleum Exporting Countries to boost their output to take pressure off soaring fuel prices at American pumps. But OPEC has since said it will maintain current production levels because crude supplies are plentiful and demand is expected to weaken in the second quarter.