President Donald Trump said on Sunday that he wanted federal law enforcement agencies to work on restoring Alcatraz, now a museum, to a functioning maximum-security prison.

Repeating one of his constant refrains that the US had become a dangerous, lawless place, Trump wrote on social media that he wanted Alcatraz, an island in San Francisco Bay, to be rebuilt “to house America’s most ruthless and violent offenders. We will no longer be held hostage to criminals, thugs, and judges that are afraid to do their job and allow us to remove criminals, who came into our country illegally”.

It was not immediately clear how his musing could be put into action, given that any such project would be extraordinarily expensive and that the administration already planned to cut billions of dollars from the justice department budget.

Trump said he had instructed the bureau of prisons, the justice department and the homeland security department to work on his idea, along with the FBI — a curious choice given that the bureau plays no role in incarcerating people convicted of crimes.

A reopened Alcatraz, Trump wrote, would “serve as a symbol of law, order, and justice”. The prison captured the public imagination as the home of the “worst of the worst” until it was closed in 1963 and turned into a popular museum attraction.

In addition to holding the gangster known as “Machine Gun Kelly” and Al Capone Alcatraz is most famous for the escape of three men in 1962. They were never found, and it remains unclear whether they survived the swim from the island, which is more than a kilometre from shore in cold water with strong currents. Today, Alcatraz is best known as a damp, frigid and nostalgic staple of tourist packages and children’s field trips.