Obama made the rare move of greeting the 79-year-old monarch at the doors of the White House, as he hailed the "longstanding friendship" between the two countries.
Salman's inaugural visit as king -- originally scheduled for May and cancelled by Riyadh -- has been billed as a way of putting relations back on a more stable footing.
In the Oval Office, Obama was effusive, saying he wanted to "once again reaffirm not only our personal friendship, but the deep and abiding friendship between our two people."
These meetings normally end in "some kind of public statement that puts as positive a spin as possible on the meeting," said Anthony Cordesman of the Center for Strategic and International Studies.
"Both nations are close strategic partners in spite of their differences, and both states need each other."
But behind the warm public statements, there are deep disagreements on Syria and Yemen as well as lingering Saudi doubts about the nuclear deal with Iran.
Saudi Arabia publicly voiced tepid support for the Iran deal, but privately expressed grave misgivings that the nuclear agreement may legitimize their arch-foe Iran.
"This is obviously a challenging time in world affairs, particularly in the Middle East," Obama said, saying the pair would discuss a "wide range of issues."
Obama said the two sides "share concerns" about the need to restore a functioning government in Yemen and relieve an urgent humanitarian crisis.
Saudi Arabia began a bombing campaign in Yemen to oust Iranian-backed rebels soon after Salman and his son and defense minister, Deputy Crown Prince Muhammad, came to power.
The United States has supported that effort, but has repeatedly warned about the impact the fighting has had on civilians.
But Saudi Arabia's backing for opposition groups like Jaysh al-Islam, an amalgam of factions that include hardline Islamists, has concerned the White House.
Riyadh views Sunni fighters as a counterbalance to the Iranian-backed Shia militias helping prop up Bashar al-Assad.
"The kingdom sees the conflict against the Iranian-supported Assad regime as an extension of the wider Persian-Arab rivalry" said Simon Henderson of the Washington Institute for Near East Policy.
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