Saudi Crown Prince Mohammed bin Salman, wearing shorts at his seaside palace, sought a relaxed tone for his first meeting with President Biden’s national security adviser, Jake Sullivan, last September.

The 36-year-old crown prince ended up shouting at Mr. Sullivan after he raised the 2018 killing of Saudi journalist Jamal Khashoggi. The prince told Mr. Sullivan he never wanted to discuss the matter again, said people familiar with the exchange. And the U.S. could forget about its request to boost oil production, he told Mr. Sullivan.

The relationship between the U.S. and Saudi Arabia has hit its lowest point in decades, with Mr. Biden saying in 2019 that the kingdom should be treated like a pariah over human-rights issues such as Mr. Khashoggi’s murder.

The political fissures have deepened since Russia’s invasion of Ukraine, senior Saudi and U.S. officials said. The White House wanted the Saudis to pump more crude, both to tame oil prices and undercut Moscow’s war finances. The kingdom hasn’t budged, keeping in line with Russian interests.

Prince Mohammed wants foremost to be recognized as the de facto Saudi ruler and future king. The crown prince runs the country’s day-to-day affairs for his ailing father, King Salman bin Abdulaziz al Saud. But Mr. Biden hasn’t yet met or spoken directly with the prince. Last summer, the president told Americans to blame low Saudi oil output for rising gas prices.

After the publication of this article online, Adrianne Watson, a White House National Security Council spokeswoman, reiterated President Biden’s stated commitment that the U.S. would support the kingdom’s territorial defense. She cited diplomatic achievements in recent weeks, such as the condemnation by Persian Gulf states, including Saudi Arabia, of Russia’s invasion of Ukraine. She said Mr. Sullivan didn’t discuss oil production with Prince Mohammed at their September meeting and that “there was no shouting.”

A Saudi official at the kingdom’s Washington embassy said after publication of this article online that the relationship between the U.S. and the kingdom remains strong. He called the meeting between Mr. Sullivan and Prince Mohammed cordial and respectful.

“Over the course of the last 77 years of Saudi-U.S relations, there have been many disagreements and differing points of view over many issues, but that has never stopped the two countries from finding a way to work together,” the official said.

The risk for the U.S. is that Riyadh will align more closely with China and Russia, or at least remain neutral on issues of vital interest to Washington, as it has on Ukraine, Saudi officials said.

The U.S.-Saudi partnership was built on the premise that the American military would defend the kingdom from hostile powers to ensure the uninterrupted flow of oil to world markets. In turn, successive Saudi kings maintained a steady supply of crude at reasonable prices, with only occasional disruptions. But the economic underpinning of the relationship has changed. The Saudis no longer sell much oil to the U.S. and are instead the biggest supplier to China, reorienting Riyadh’s commercial and political interests.

U.S. officials, including White House Middle East coordinator Brett McGurk, have visited the kingdom repeatedly to try to heal the breach, with an eye to addressing Saudi concerns about security threats from Iran and the Houthi rebels Iran backs in Yemen. Yet with Mr. Biden opposed to any broad concessions to the Saudis, the officials acknowledge making only modest progress.

The White House has stopped asking the Saudis to pump more oil. Instead, it asks only that Saudi Arabia not do anything that would hurt the West’s efforts in Ukraine, a senior U.S. official said.

The Saudis cut short a high-level military delegation to Washington last summer and called off a visit last fall by Defense Secretary Lloyd Austin. A planned visit last month by Secretary of State Antony Blinken was canceled.