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Several members of the all-male Saudi delegation refused to shake First Lady Michelle Obama's hand.
The leaders also tackled the issue of Iran's nuclear programme and human rights in the conservative kingdom, a senior US official said.
There has also been unease in the kingdom about Mr Obama's pursuit of a nuclear deal with Shiite-dominated Iran, the regional rival of Sunni-majority Saudi Arabia.
Members of the 29-member bipartisan US delegation, which 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."
The Americans arrived for a four-hour stop from India, where Mr Obama cut short a state visit following the death Friday of Salman's predecessor, King Abdullah.
Saudi television showed Salman, 79, welcoming Mr Obama and his wife Michelle at the bottom of a red-carpeted ramp before a military band played the US and Saudi national anthems.
US President Barack Obama and first lady Michelle descend from Air Force One upon their arrival in Saudi Arabia. Photo / AP
In contrast to Saudi women, required to dress head-to-toe in black, Mrs Obama wore dark slacks and a blue top with her hair uncovered.
Crown Prince Moqren and Mohammed bin Nayef, the powerful interior minister who is second in line to the throne, were among those greeting 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 heavily in the air.

