But the plan was revived, and last month the company’s chief financial officer told investors that it was prepared for a stock listing. The company had already been increasing its financial openness and clarity for the sake of international investors. The suggestion that it was ready for a public offering came during its first-ever earnings call.

[Read more: Saudi Aramco Says It’s ‘Ready’ for I.P.O. as It Reports Half-Year Earnings]

The renewed interest in an I.P.O. suggests that the crown prince thinks that the storm of controversy over Mr. Khashoggi’s killing is passing and that he is ready to move ahead with his plans.

The Public Investment Fund, which Mr. al-Rumayyan will continue to lead, would most likely receive proceeds from any Aramco stock that the Saudi government holds. The fund is turning into a “kind of national development bank” for carrying out the crown prince’s projects, said Karen Young, a resident fellow at the American Enterprise Institute, a research firm based in Washington.

Aramco still needs to decide where to list the company, potentially a huge trophy for any exchange. To Aramco and the Saudis, the choice of where to list the stock is in many ways the more important part of the I.P.O. process, some observers say.

“It is not just about financial results,” said David Buck, a Houston-based partner at the law firm Sidley Austin, who specializes in oil company work. The terms of the public offering, including Aramco’s choice of an exchange, he said, will be “a commentary on both the company and the country.”

Aramco has said that it wants to float its stock on both Saudi Arabia’s stock exchange in Riyadh, known as the Tadawul, and a major international market. The Saudi exchange has been fortifying its technology resources to handle the huge amount of trading that an Aramco listing would bring.

What has drawn the most attention is where Aramco will choose to list its shares outside the Middle East. But amid the choices are potential pitfalls for the company.