The allies have longstanding ties and remain bound by shared interests in regional stability and oil.
But analysts say Riyadh has grown dissatisfied with what it sees as a lack of US engagement with regional crises as Washington looks to Asia.
Members of the US delegation, which crossed party lines and included former Bush-era officials, said they wanted to show support for the US-Saudi relationship.
"I believe it is important that we demonstrate to the Saudis the importance that they represent to us," said James Baker, secretary of state during the first Gulf War against Iraqi dictator Saddam Hussein.
"This is an extraordinarily critical and sensitive time in the Middle East when everything seems to be falling apart. And the kingdom in some way is becoming an island of stability," said Baker.
Obama and his 29-member delegation arrived for a four-hour stop from India where he cut short a state visit after the death of Salman's predecessor, King Abdullah, on Friday.
Saudi television showed Salman, 79, welcoming Obama and his wife Michelle at the bottom of a red-carpeted ramp before a military band played the US and Saudi national anthems.
In contrast to Saudi women, required to dress head-to-toe in black, Michelle Obama wore dark slacks and a blue top with her hair uncovered.
Salman's heir Crown Prince Moqren and Mohammed bin Nayef, the powerful interior minister who is second in line to the throne, were among those who greeted the Americans.
The US president then boarded a black limousine taking him for talks and dinner with Salman at central Riyadh's Erga Palace, the king's private residence where the smell of incense hung heavy in the air.
Authorities deployed armoured vehicles, police cars and radar along streets in the city to secure Obama's visit, an AFP reporter observed.
Deputy National Security Adviser Ben Rhodes said the trip was an "opportunity to both pay respects to the legacy of King Abdullah, who was a close partner with the United States and also to touch base on some of the issues where we're working together with the Saudis," which include the Islamic State group extremists, Yemen, and the Iranian nuclear negotiations.
Obama last visited Saudi Arabia in March, when he held talks with Abdullah.
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- A 'major bulwark' -
Former national security adviser Brent Scowcroft and Condoleezza Rice, secretary of state under George W. Bush, were among the US contingent which included current Central Intelligence Agency director John Brennan and General Lloyd Austin, head of US Central Command.
They had all been with Obama in India but Secretary of State John Kerry and Senator John McCain joined the president especially for his Saudi trip.
McCain, a Republican, chairs the Senate Armed Services Committee, and had been in Saudi Arabia as part of a Middle East tour several days ago.
During that trip he called for "additional US boots on the ground in Iraq and Syria" to defeat the Islamic State group which has seized territory there and been accused of widespread atrocities.
Saudi Arabia is part of a US-led coalition conducting air strikes against the militants.
The SITE Intelligence Group monitoring service said Tuesday that IS released a video celebrating the death of the "tyrant Abdullah" and said that "Allah permitting" they will invade the Arabian Peninsula soon.
McCain said the kingdom was emerging "as the major bulwark" against efforts by Iran to expand its influence in Syria, Iraq, Lebanon, Yemen and Bahrain.
Shiite-dominated Iran is the regional rival of Sunni-majority Saudi Arabia.
"There is no doubt that the Iranians are on the move," McCain said, adding it was appropriate to be part of this visit "given relations over here and the importance of Saudi Arabia."
The 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."
Obama is the latest leader to visit Riyadh since Friday.
His welcome was the most elaborate but sheikhs, presidents and prime ministers from Europe, Asia, Africa and the Americas, all came to pay their respects.
It is a recognition of the kingdom's power as the world's leading oil exporter, a political heavyweight in a region threatened by extremist violence, and as home to Islam's holiest sites.
Australia's Governor General Peter Cosgrove also arrived on Tuesday.