A Saudi official said after Cheney met the Saudi monarch on Tuesday: "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."
The two men agreed on "the need for Syria to cooperate with the UN probe [into the murder of former Lebanese prime minister Rafiq al-Hariri] in keeping with UN Security Council resolutions and on the importance of safeguarding security in the region", he added, requesting anonymity.
Cheney, who was due to travel on to Kuwait to pay his respects after the death of its amir, Shaikh Jaber al-Ahmad al-Sabah, later met Lebanese MP Saad al-Hariri.
Al-Hariri is the son of the former Lebanese prime minister whose February 2005 assassination triggered anti-Damascus protests and led to the end of Syria's 29-year military presence in Lebanon.
Saad al-Hariri has since spent most of his time in Saudi Arabia, where his late billionaire father once made his fortune, due to security concerns.
Riyadh and Cairo have been trying to ease Syria-Lebanon tensions after the assassination of al-Hariri and attacks on a number of anti-Syrian Lebanese figures widely blamed on Damascus.
Western powers, Washington and Paris in particular, have been turning up the heat on Damascus since a UN investigation implicated Syria in the Beirut bomb blast which killed al-Hariri and 22 other people.
"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"
Earlier, Cheney had discussed tensions between Syria and Lebanon with Mubarak in Cairo.
Mubarak's spokesman said: "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."
The Saudi official said King Abdullah voiced satisfaction at US efforts to facilitate the Palestinian elections on 25 January.
Abdullah stressed the need for Washington to help the Palestinian Authority and pursue its efforts to "implement the road map and achieve the US president's 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.
Abdullah and Cheney 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 said co-operation in the fight against terrorism was also on the agenda.