The U.S. isn’t currently planning any significant changes to the number of U.S. forces stationed in Saudi Arabia but some aspects of the two nations’ extensive defense cooperation could be affected following President Biden’s decision to reassess relations after OPEC+ unveiled an oil production cut, U.S. officials said.

The officials said that the U.S. relationship was too critical to American interests in the Middle East to change the overall course and that the U.S. was determined to continue its strategic cooperation with Riyadh that is central to combating Iran. But there could be a decline in some areas of defense cooperation.

Last week, for instance, the U.S. canceled its participation in a working group between the U.S. and the Gulf Cooperation Council on Iran, which was scheduled to take place Oct. 17, U.S. officials said. The meeting was to focus on integrating defense among regional allies, in particular missile defense.

The officials added that the U.S. could also slow some of the huge amounts of arms sales that Saudi Arabia engages in annually to send a message of U.S. displeasure.

Many Democratic lawmakers have called for those sales to stop but any congressional action to force a halt is unlikely to have the votes to pass in Congress. U.S. and European defense officials say those sales—which have amounted to at least $130 billion of proposed or completed military sales since 2010—provide an enduring and tangible link to maintaining Saudi relations.

“The Saudis are trying to make their military more like our military, and the Pentagon sees that as an important initiative,” said Jon Alterman, who directs the Middle East program at the Washington-based Center for Strategic and International Studies.

The U.S. officials added that harming the military relationship could make countering Iran, improving Saudi-Israeli relations and resolving other regional issues more challenging. There already has been an erosion in some aspects of the two nations’ defense cooperation, and officials said it was important that they not deteriorate further. Otherwise, Saudi Arabia may conclude that Chinese and Russian military support is enough to rely on for defense against the kingdom’s top foe, Iran, creating a new alliance with U.S. rivals that would greatly concern the West, the officials said.

U.S. forces have trained their Saudi counterparts, advised them on their military operations and in the past supported Saudi forces in the kingdom’s war in Yemen with arms, refueling and advice, though that cooperation has diminished in recent years. About 3,000 U.S. troops are currently based in Saudi Arabia.

“On the military side, I can’t imagine that the U.S. is going to stop training [Saudi forces] because it’s not in our interest to not have the Saudis better trained,” said Jonathan Panikoff, director of the Atlantic Council’s Scowcroft Middle East Security Initiative, a think tank. He added that intelligence sharing also is likely to continue: “Stopping cooperation there would undermine U.S. national security.”

In a statement released on Twitter, the Saudi foreign ministry said the government views its relationship with the U.S. as “a strategic one that serves the common interests of both countries.”

“The Kingdom also stresses the importance of building on the solid pillars upon which the Saudi-U.S. relationship had stood over the past eight decades,” the statement read. “These pillars include mutual respect, enhancing common interests, actively contributing to preserve regional and international peace and security, countering terrorism and extremism, and achieving prosperity for the peoples of the region.”

The U.S.-Saudi relationship has been on rocky ground since Mr. Biden took office last year, given his decision to renegotiate a nuclear deal with Iran and his public condemnation of Saudi Arabia as a pariah state.

Mr. Biden’s visit to Saudi Arabia this summer signaled his intention to work closely with the kingdom on a range of issues, particularly energy cooperation, despite criticism from some within his own Democratic Party that he was turning a blind eye to the kingdom’s human-rights record.

Then last week, the Organization of the Petroleum Exporting Countries and its Russia-led allies, known as OPEC+, agreed to an oil production cut of 2 million barrels a day after months of U.S. public and private pleas that such a move would have serious consequences amid a global energy crisis.

Mr. Biden said afterward that the U.S. would reassess its relationship with the Saudis but didn’t provide specifics. Some U.S. officials said they viewed the cut as a swipe at the administration ahead of November’s midterm elections when control of Congress is at stake.

U.S. lawmakers reintroduced a bill to immediately suspend arms sales to Saudi Arabia. And three Democratic legislators introduced a bill that would remove U.S. troops from Saudi Arabia and another 2,000 U.S. troops from the U.A.E., as well as military equipment like the Patriot and Terminal High Altitude Area Defense systems that Riyadh uses.

“We see no reason why American troops and contractors should continue to provide this service to countries that are actively working against us,” the legislators wrote in a statement, adding that Saudi Arabia and the U.A.E. were effectively aiding Russian President Vladimir Putin in his invasion of Ukraine with a move that was designed to support the global price of oil.

Congressional officials said the bills are unlikely to pass as there is no consensus on Capitol Hill about how to respond to the OPEC+ decision or even whether Saudi Arabia should face a U.S. response. Some legislators have proposed improving domestic oil and gas production instead. Others don’t want cooperation affected in any way. Sen. Joni Ernst (R., Iowa) in a Wednesday letter to national security adviser Jake Sullivan, viewed by The Wall Street Journal, said canceling the GCC meeting “delays partner capacity, worsens regional security, and aids our adversaries.”

Although military ties are likely to be little-affected by the recent tensions, they have diminished in some important aspects in recent years as tensions between the two nations have increased. Mr. Biden has criticized the country over human-rights abuses and the killing of journalist Jamal Khashoggi, which the American intelligence community concluded was ordered by Crown Prince Mohammed bin Salman.

The U.S. also has ended operational support for Saudi military operations in Yemen, which Saudi Arabia has complained weakens their negotiating position with the Houthis they have been fighting. And the U.S. has reduced the number of troops in the region. After the U.S. military abruptly withdrew from Afghanistan last year, Gulf nations including Saudi Arabia feared the U.S. was leaving the Middle East to focus on China.

A year ago, the Saudis abruptly canceled a meeting with Defense Secretary Lloyd Austin without an explanation. Hours later, the Saudis released a photo on social media showing Saudi national security officials meeting instead with Russian officials.

During a visit in May to Saudi Arabia by the head of U.S. Central Command, Army Gen. Erik Kurilla, U.S. aircrews transporting the general prepared for two flight routes—to Prince Sultan Air Base, where U.S. troops were stationed, and to Jeddah, where Crown Prince Mohammed was staying on the off-chance a visit would happen. Gen. Kurilla eventually flew to the air base. Neither Gen. Kurilla nor Secretary Austin have met face-to-face with the crown prince.