Saudi Arabia's Crown Prince Salman bin Abdul Aziz will take over as the new king, but he is in poor health and his reign may not last long. (Yuya Shino/Reuters)

Saudi Arabia’s King Abdullah bin Adbul Aziz died early Friday, setting the stage for a transition of power at a critical moment as the key U.S. ally in the Middle East struggles with falling oil prices and rising Islamist violence.

The monarch, believed to be 90, was succeeded by his brother, Crown Prince Salman, according to state television. That put the region’s most important Sunni power and America’s closest Arab ally in the hands of a 79-year-old who is reportedly in poor health.

[Read obit: Abdullah, a wily king who embraced limited reform, dies]

Salman’s rise to the throne postpones the question of when the Saudi monarchy will turn to the next generation of princes to run their country of 28 million people at a crucial moment in a region mired in crisis.

While observers in Riyadh widely predicted a smooth transition to Salman, his poor health means his rule could be relatively short. Should there be a power struggle to succeed him, it could leave a vacuum in the Middle East at a critical time. Saudi Arabia is a key member of the U.S.-led coalition against the Islamic State and a major ally of the government that just fell in neighboring Yemen.

“Despite so many people saying it will be a smooth transition, there’s every reason to believe that Saudi Arabia is heading for rough times,” Simon Henderson, an expert on the Saudi succession at the Washington Institute for Near East Policy, said in an interview Thursday.

[View: The Saudi royal family tree]

“Yemen is falling apart, ISIS is knocking at the door . . . this is an extraordinarily dangerous Middle East from a Saudi perspective,” Henderson added.

By Saudi tradition, the crown passes down among the sons of national founder King Abdulaziz bin Saud, who died in 1953. Salman would be the sixth son of Abdulaziz to be king, and few of his remaining brothers — out of at least 35 who were alive when Abdulaziz died — are believed to be healthy or qualified to assume the throne.

In an apparent bid to preempt quarrels about succession — and also secure the line for his own favored branch of the family — Abdullah last year took the unprecedented step of anointing a deputy heir, Prince Muqrin, 71, his youngest brother.

Muqrin is said to be smart and is well-liked by ordinary Saudis; he also has good ties with Saudi Arabia’s most important ally, the United States. But the choice sparked fierce opposition from some of the many excluded princes, who complained that Abdullah was defying a tradition that allows each king to name his own heir. Additionally, Muqrin’s mother was a Yemeni concubine, not a Saudi princess, and some in the family reportedly consider his lineage too impure for him to wear the crown.

By Saudi tradition, King Salman would be free to choose his own successor-in-waiting, but it is widely believed here that he would simply elevate Muqrin from deputy to crown prince.

At that point, the Saudi royal family would face a far more complicated puzzle about who would succeed Muqrin, but it would almost certainly be a prince from the next generation, the grandchildren of Abdulaziz. Hundreds of princes belong to that generation.

[From the archive: Succession stirs controversy in Saudi Arabia]

The succession process is conducted by the Allegiance Council, a body created by Abdullah. It consists of 35 senior princes, all sons and grandsons of Abdulaziz, who meet in secret to choose a new leader when the king dies.

The vast al Saud family is believed to be riven by factions. But historically, the family has managed to come together with the primary goal of preserving their iron rule.

Even if the feuds are contained behind palace doors, though, the squabbles could paralyze decision-making in the kingdom at a critical time.

Henderson said there could be far more maneuvering than the royal family will admit. He said some would privately argue that Salman is not of sound enough mind to run the country, and other factions would push their own favorites.

“The trick is always to try and understand their logic and not be too confined by our own logic,” he said. “Their logic is different. They hate the idea of public show of disunity. So they’ll try to cover that up completely.”

Henderson said “Western logic” would suggest that the Saudis would be smarter to pass over Salman in favor of Muqrin or a next-generation king to lead the country at an increasingly complex and violent time. Saudi borders a part of Iraq where the Islamic State is influential, and its southern neighbor, Yemen, is in the midst of a power struggle that Saudis believe will strengthen Iran, its regional rival.

“The problem is we have only our perspective on who counts, and it’s not an insider’s perspective,” Henderson said.

Correction: This article has been amended to correct an earlier, unverified characterization of King Salman’s mental health. The article’s assertion that King Salman was “reportedly … suffering from dementia’’ was too speculative and unsubstantiated to meet The Post’s standards for publication.  The Royal Court of Saudi Arabia, through its lawyers, has asserted to The Post that King Salman is “most certainly not suffering from dementia or any other kind of mental impairment.’’

Sly reported from Beirut.