"The talks covered the situation on the Syrian and Lebanese scenes and Saudi-Egyptian efforts to ward off an escalation of the situation in the region," a Saudi official told AFP after Mr Cheney met the Saudi monarch.
The two men agreed on "the need for Syria to cooperate with the UN probe (into the murder of former Lebanese prime minister Rafiq Hariri) in keeping with UN Security Council resolutions and on the importance of safeguarding security in the region," he said.
Mr Cheney was also due to meet with Lebanese MP Saad Hariri later at Riyadh airport before travelling on to Kuwait to pay his respects after the death of its emir, Sheikh Jaber al-Ahmad al-Sabah.
Saad Hariri is the son of the former Lebanese premier whose February 2005 assassination triggered anti-Damascus protests and led to the end of Syria's 29-year military presence in Lebanon.
Saad Hariri has since spent most of his time in Saudi Arabia, where his late billionaire father once made his fortune, due to security concerns.
Ease tensions
The governments in Riyadh and Cairo have been trying to ease Syria-Lebanon tensions after the assassination of Mr Hariri and a number of anti-Syrian Lebanese figures that have been widely blamed on Damascus.
Western powers, Washington and Paris in particular, have been turning up the heat on Damascus, since a UN investigation into the Beirut bomb blast which killed Mr Hariri and 20 other people implicated Syria in the murders.
Washington has threatened the government in Damascus with more Security Council action and accused President Bashar al-Assad's regime of obstructing the UN probe.
Earlier, Mr Cheney discussed tensions between Syria and Lebanon with Mr Mubarak in Cairo.
"We cannot say that today's meeting brought about any solutions in this file, because it is not so simple and any solution should be based on the implementation of Security Council resolutions," Mr Mubarak's spokesman said.
The Saudi official said King Abdullah voiced satisfaction at US efforts to "facilitate" the legislative elections in the Palestinian territories on
January 25.
Washington help
King Abdullah stressed the need for Washington to help the Palestinian Authority and pursue its efforts to "implement the roadmap and achieve the US president's (George W. Bush) vision about the establishment of an independent Palestinian state."
The two leaders also reviewed "efforts and contacts under way at the Arab and local levels to ensure the success of the political process in Iraq," the official said.
Saudi Arabia and Egypt are co-sponsors of an Iraqi reconciliation conference to be held in Baghdad in late February or early March in a bid to bring the disempowered Sunni Muslim community back into the political arena.
King Abdullah and Mr Cheney also examined the Iranian nuclear file, the official said, as Western powers step up their threat to refer Tehran to the Security Council over its resumption of sensitive nuclear fuel research work.
Saudi officials earlier said that cooperation in the fight against terrorism was also on the agenda.
The vice president had kicked off his regional tour in December but cut it short to deal with a domestic issue.