Abd Allah and other Saudi officials met Vice-President Dick Cheney in Dallas on the eve of the meeting with Bush, which is expected to produce statements about cooperation between the two countries.
Saudi Arabia's image in the US has been tarnished by the fact that 15 of the 19 hijackers in the 11 September 2001 attacks were Saudi citizens and alleged members of the al-Qaida network led by Usama bin Ladin who was also born in Saudi Arabia.
The kingdom has disavowed Bin Ladin and is battling a homegrown al-Qaida-related insurgency of its own.
The US invasion of Iraq in 2003 angered Saudi Arabians, but US-Saudi ties strengthened after the kingdom took steps to capture or kill senior al-Qaida members within its borders.
"We need the Saudis and they need us, despite the poor image of the United States in Saudi Arabia and their poor image here," said David Mack, vice-president at the Middle East Institute.
On the economic front, the White House is facing growing consumer dissatisfaction over rising oil prices, with retail gasoline hitting a record nationwide average of $2.28 a gallon this month.
Bush is expected to press for more oil production from Saudi Arabia, the biggest producer within the Organisation of Petroleum Exporting Countries (Opec).
Saudi Arabia has been battling
with al-Qaida linked fighters
Democratic Representative Edward Markey of Massachusetts blamed the Bush administration for a "failed energy policy", and called for a plan that focused on renewable technologies, energy efficiency and conservation rather than an expansion of oil and gas drilling in the United States.
The House of Representatives has approved an $8 billion energy bill with incentives to increase domestic production of crude oil, natural gas, coal, nuclear and other energy sources.
It would allow oil drilling in Alaska's Arctic National Wildlife Refuge. The Senate was expected to complete its version of the bill in May.
The Saudis are hoping for an agreement that would pave the way for the kingdom to join the World Trade Organisation. Officials have been working around the clock to see if the last
sticking points can be ironed out so it can be announced at the Bush-Abd Allah meeting.
The United States wants barriers eased to allow more US corporate participation in the Saudi insurance, financial services and telecommunications markets.
Democracy on the agenda
Bush also planned to discuss his efforts to promote democracy and peace in the Middle East as well as the battle against terrorism.
In his February State of the Union speech, Bush mentioned Saudi Arabia as one of the countries that had captured or
detained al-Qaida fighters.
Saudi Arabia says it has killed more than 90 armed fighters behind the bombings and shootings that have killed civilians and security personnel in the past two years.
"They have been rooting out al-Qaida sympathisers, organisers in their country," a former US intelligence official said. "They've been knocking off senior guys."
The Saudis also want the United States to play a stronger role in the peace process between Israelis and Palestinians, and that issue is likely to be discussed at the meeting.