Secretary of State Antony J. Blinken said during an online event last week that Mr. Biden came into office intending to ensure that the U.S. relationship with Saudi Arabia “was serving our own interests, as well as our values, as we move forward.”

“But also preserving it,” Mr. Blinken added, “because it also helps us accomplish many important things.”

He did not mention Saudi Arabia’s growing military and security ties to China, the country that he and Mr. Biden have both said is the greatest long-term challenger to the United States.

Separately, an advocacy group of close relatives of people killed in the Sept. 11, 2001, attacks is using the prospect of a trip by Mr. Biden to Saudi Arabia to increase pressure on the U.S. government to grapple with links between Saudi government officials and the hijackers. On Tuesday, the family members sent government leaders two letters on the topic with about 1,800 signatures, according to an organizer of the effort, Brett Eagleson, whose father was killed in the south tower of the World Trade Center.

The first letter, addressed to Congress, asks for an oversight hearing to scrutinize links between Saudi government officials and the Sept. 11 plot. The second letter, addressed to Mr. Biden and Mr. Blinken, asks for the State Department to take the extraordinary step of designating Saudi Arabia as a state sponsor of terrorism, which would expose the oil-rich nation to economic sanctions.

“After nearly 21 years, we are as determined as ever to hold the Kingdom of Saudi Arabia accountable for its role in the mass murder of our loved ones,” they wrote in both letters.

Last year, ahead of the 20th anniversary of the attacks, the Sept. 11 family members pressured Mr. Biden to declassify materials from the government’s scrutiny of Saudi links. Mr. Biden issued an executive order that has resulted in rolling releases of such materials. The letters cited excerpts, including a 130-page overview the F.B.I. wrote in July 2021 that stated that an investigation determined that two hijackers were assisted by a network centered on offices affiliated with the Saudi government, including its Los Angeles consulate.

Charlie Savage contributed reporting.