“Not only is it an attack on the private sector, which is being touted to help promote growth in the Saudi economy, but it is also focused on the petrochemical sector, which is a core part of the Saudi economy,” said Amy Myers Jaffe, an expert on Middle East energy at the Council on Foreign Relations.

Saudi Arabia has cut oil exports in recent years to support global oil prices, a strategy central to its efforts to make a potential public offering of shares of government-controlled Saudi Aramco more attractive to international investors. The kingdom has tried to compensate for its lost revenue by expanding its petrochemical and refining industry.

Some technical details of the attack in August have been previously reported, but this is the first time the earlier attacks on Tasnee and other Saudi petrochemical companies have been reported.

Security analysts at Mandiant, a division of the security firm FireEye, are still investigating what happened in August, with the help of several companies in the United States that investigate cyberattacks on industrial control systems.

A team at Schneider Electric, which made the industrial systems that were targeted, called Triconex safety controllers, is also looking into the attack, the people who spoke to The Times said. So are the National Security Agency, the F.B.I., the Department of Homeland Security and the Pentagon’s Defense Advanced Research Projects Agency, which has been supporting research into forensic tools designed to assist hacking investigations.

All of the investigators believe the attack was most likely intended to cause an explosion that would have killed people. In the last few years, explosions at petrochemical plants in China and Mexico — though not triggered by hackers — have killed several employees, injured hundreds and forced evacuations of surrounding communities.

What worries investigators and intelligence analysts the most is that the attackers compromised Schneider’s Triconex controllers, which keep equipment operating safely by performing tasks like regulating voltage, pressure and temperatures. Those controllers are used in about 18,000 plants around the world, including nuclear and water treatment facilities, oil and gas refineries, and chemical plants.