His corruption purge at home, meanwhile, risks alienating parts of the royal family and the financial elite at a moment that would appear to demand unity, either to smooth a succession or to face off against Iran. As many as 17 people detained in the anti-corruption campaign have required medical treatment for abuse by their captors, according to a doctor from the nearest hospital and an American official tracking the situation.

The former Egyptian security chief, Habib el-Adli, said by one of his advisers and a former Egyptian interior minister to be advising Prince Mohammed, earned a reputation for brutality and torture under President Hosni Mubarak. His lawyers say he plans to appeal his recent sentence in absentia in Egypt to seven years in prison on charges of corruption.

Officials of the Saudi Royal Court referred press queries about these reports to the Embassy of the Kingdom of Saudi Arabia in Washington, where a spokeswoman, Fatimah Baeshen, said the embassy could not confirm or dispute them.

With the decline in the price of oil in recent years, Saudi Arabia has frozen projects and spent more than a third of its financial reserves, draining them to about $475 billion this fall from a peak of $737 billion in August 2014. At that burn rate, the kingdom has only a few years to lift its revenue or slash its spending to forestall a financial crisis.

Against that backdrop, the prince’s supporters argue that the anti-corruption campaign aims to recapture hundreds of billions of dollars that have leaked from the state budget through graft and self-dealing — money he needs to fund his development plans.

Prince Mohammed had appealed to the kingdom’s wealthy for months to invest in his modernization program. But some groused that his plans — like a new $500 billion business hub “for the dreamers of the world,” built from scratch and fueled entirely by clean energy — were ill-conceived and grandiose, and instead of investing at home they quietly moved their assets abroad.