Saudi Arabia has been a dealmaking machine in recent years, dangling the prospect of hundreds of millions of dollars in fees to banking advisers on Wall Street and in London. The kingdom’s $320 billion sovereign-wealth fund, the Public Investment Fund, holds significant positions and board seats in companies like the ride-sharing service Uber and the Japanese media and technology conglomerate SoftBank. The initial public offering of Saudi Arabia’s huge oil company, Saudi Aramco, is expected to be the largest deal of its kind.

This year’s Future Investment Initiative begins next Tuesday at Riyadh’s lavish Ritz-Carlton hotel with discussions of the global economy and issues of work force inclusion. But some executives plan to arrive earlier and attend private events with Yasir al-Rumayyan, the governor of the Public Investment Fund and the recently appointed chairman of Aramco, and other officials.

Mr. Mnuchin is expected to participate in a moderated discussion during the main portion of the conference. He initially planned to attend last year, but reversed that decision as international anger grew over the killing.

Some business leaders have signaled their hopes for a better human-rights record in Saudi Arabia, whose government also imprisoned hundreds of elites in the Ritz-Carlton as part of a purported crackdown on corruption in November 2017. During months of captivity at the luxury hotel, some were subjected to coercion and physical abuse, a New York Times investigation found.

In a LinkedIn post this year, Mr. Fink pledged to help continue BlackRock’s dialogue with Saudi leaders in hopes that economic diversification would help the country modernize its economy and society. Still, his statement carried a tacit warning: “As I have said repeatedly to Saudi leaders,” he wrote, “for Saudi Arabia to be on the world stage, it must act like a world leader.”

Other executives have been less charitable about their relationships with Saudi Arabia. Earlier this year, the talent and media company Endeavor severed its relationship, returning $400 million Saudi Arabia had invested in it as a protest of Mr. Khashoggi’s murder.

The Trump administration, which has counted Saudi Arabia as a critical ally in the Middle East, has walked a fine line in reacting to human-rights issues. While Mr. Mnuchin did not attend last year’s conference, for instance, he still traveled to Riyadh and met with Prince Mohammed, where they discussed economic ties and counterterrorism initiatives, as well as the investigation into Mr. Khashoggi’s death.