But according to people inside the Saudi government, Mr. Biden’s July visit did little to change Prince Mohammed’s determination to chart a foreign policy independent of U.S. influence, in a break from almost 80 years of American-Saudi partnership.

If anything, said the people inside the Saudi government, the visit angered Prince Mohammed, who was upset that Mr. Biden went public with his private comments to the Saudi royal over Mr. Khashoggi’s death, which prompted Saudi officials to publicly contradict Mr. Biden’s characterization of their interaction. …

Prince Mohammed has told advisers that he isn’t willing to sacrifice much for the Biden administration, said the people inside the Saudi government, citing its critical view of the Saudi war in Yemen, bid to close a nuclear deal with Iran that Riyadh opposes and Mr. Biden’s own comments on the prince.

In August, the Saudis had planned to push OPEC+ to raise oil production by 500,000 barrels a day in an effort to please Mr. Biden, but Prince Mohammed ordered the increase lowered to a token 100,000 barrels a day after the Biden visit, the people inside the Saudi government said.

The U.S. State Department’s energy-security envoy, Amos Hochstein, sent the Saudi energy minister, Prince Abdulaziz bin Salman, an email that suggested he had broken his word promising a larger increase, people familiar with the matter said.

The email angered Prince Abdulaziz and strengthened his resolve to forge an oil policy independent of the U.S., the people said.