Obama cut short a state visit to India to pay his respects to new King Salman, 79, after Abdullah died on Friday aged about 90.
The United States established full diplomatic relations with the conservative Muslim kingdom in 1940 and the unlikely allies remain bound by shared interests in regional stability and oil.
Despite the longstanding partnership, analysts say Riyadh has grown dissatisfied with what it sees as a lack of US engagement with key regional issues as Washington looks to Asia.
Anwar Eshki, chairman of the Jeddah-based Centre for Strategic and Legal Studies, said "divergences persist" between the two countries.
The differences include the battle against the Islamic State group in Iraq and Syria, the nearly four-year-old rebellion against the Damascus regime and the post-Arab Spring chaos in Libya and Yemen.
Riyadh would like Washington to exercise more pressure to get the rival sides in both Yemen and Libya back to the negotiating table, Eshki said.
Libya has two rival governments and powerful militias are battling for territory.
In Yemen, on Saudi Arabia's southern border, President Abdrabuh Mansur Hadi, a key US ally in the fight against Al-Qaeda, tendered his resignation last week after Shiite militiamen kidnapped his chief of staff and seized the presidential palace.
Salman Shaikh, director of the Brookings Doha Centre, said "the relationship is not what it was".
Ties were better under both George Bush and his son George W Bush, who had a "relationship that was very much built on personal foundations," Shaikh contended.
The late king had a strained personal relationship with Obama, said Frederic Wehrey, of the US-based Carnegie Endowment for International Peace Middle East Programme.
Among the 29 members of Obama's delegation are former Bush-era officials including James Baker, secretary of state during the first Gulf War against Iraqi dictator Saddam Hussein, former national security adviser Brent Scowcroft, and Condoleezza Rice, who served as secretary of state under George W. Bush.
Obama's wife Michelle is to join him on the Saudi trip, as is Secretary of State John Kerry, Senator John McCain, Central Intelligence Agency director John Brennan and General Lloyd J. Austin III, head of US Central Command.
The four-hour stopover is to include bilateral talks between Obama and Salman, followed by a dinner.
Deputy National Security Adviser Ben Rhodes confirmed in New Delhi that the turmoil in Yemen and the battle against IS would figure on the agenda.
"I'm sure that while we are there, they will touch on some of the leading issues where we cooperate very closely with Saudi Arabia," he said.
"Clearly that would include the continued counter-ISIS campaign where the Saudis have been a partner and have joined us in military operations," he said, using an alternative acronym for IS.
"That of course also includes the situation in Yemen where we have coordinated very closely with Saudi Arabia and the other countries."
The Saudi royal court said Salman would hold talks with Obama on "regional and international issues of common interest, in addition to means of enhancing bilateral relations."
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