Cheney arrived in Riyadh, the Saudi capital, on Saturday. His one-day visit to the kingdom comes as violence continues unabated in Iraq.
Saudi Arabia and the US have been close allies, but the partnership has been tested after the September 11, 2001, attacks and the US' invasion of Iraq in 2003.
Güncelleme Tarihi: 20 Eylül 2018, 18:16
On Thursday, more than 200 people were killed in a Shia neighbourhood in the Iraq capital, prompting a new political crisis ahead of next week's talks in Jordan between Nuri al-Maliki, the Iraqi president, and George Bush, the US president.
Other developments in Iran, Lebanon and the Palestinian territories have added to instability in the Middle East and are expected to be on the agenda of Cheney's talks with Abdullah.
Edmund Ghareeb of American University in Washington told Al Jazeera: "Saudi Arabia has connections with a number of regional players, so probably the United States is going to focus on Saudi Arabia, maybe providing financial assistance to help with the reconstruction in Iraq as well as the political contacts."
Talks are also expected to treat Iran's nuclear programme that the US and some of its Western allies believe aims to produce an atomic weapon. Iran has denied the accusations.
Adel Darwish, associate editor of Middle East magazine, told Al Jazeera that Saudi Arabia is instrumental in the US' bid to keep a check on Iran's nuclear capability.
"[The US] would need the Saudis on board. They are the biggest Muslim Sunni influence in the Muslim world to counter-balance the Iranian [Shia] influence. There is worry in Saudi Arabia about Iran's nuclear programme," he said.
The US denied reports that Cheney had visited Iraq earlier in the week.