Donald Trump says he is directing his government to reopen and expand Alcatraz, the infamous former prison on an island near San Francisco's Golden Gate Bridge.

In a message on his Truth Social site on Sunday, President Trump said that "for too long America has been plagued by vicious, violent, and repeat criminal offenders".

The reopening of Alcatraz - once notorious as one of the US's toughest prisons - would serve as a "symbol of law, order, and justice," he said.

Leading Democrats said the proposal was "not a serious one". The maximum security facility, also known as The Rock, was closed in 1963 and it is currently operating as a successful tourist site.

"Today, I am directing the Bureau of Prisons, together with the Department of Justice, FBI, and Homeland Security, to reopen a substantially enlarged and rebuilt ALCATRAZ," Trump wrote.

The prison would "house America's most ruthless and violent Offenders".

President Trump has been clashing with the courts over his policy of sending alleged gang members to a prison in El Salvador. In March, he sent a group of more than 200 alleged Venezuelan gang members there. He has also talked about sending "homegrown criminals" to foreign prisons.

Alcatraz was originally a naval defence fort, and it was rebuilt in the early 20th Century as a military prison. The Department of Justice took it over in the 1930s and it began taking in convicts from the federal prison system. Among its more famous inmates were the notorious gangsters Al Capone, Mickey Cohen and George "Machine Gun" Kelly.

The prison was also made famous by the 1962 film, Birdman of Alcatraz, starring Burt Lancaster, about the convicted murderer Robert Stroud, who while serving a life sentence on the prison island developed an interest in birds and went on to become an expert ornithologist.

In 1979, the American biographical prison drama Escape from Alcatraz recounted a 1962 prisoner escape with Clint Eastwood starring as ringleader Frank Morris.

It was also the site of the 1996 film The Rock, starring Sean Connery and Nicolas Cage, about a former SAS captain and FBI chemist who rescue hostages from Alcatraz island.

The prison closed because it was too expensive to continue operating, according to the Federal Bureau of Prison website. It was nearly three times more costly to operate than any other federal prison, largely due to its island location.

It would take an enormous amount of money to make Alcatraz into a functioning prison, Professor Gabriel Jack Chin from the Davis School of Law at the University of California told the BBC.

The federal prison system is actually down about 25% from its peak population and "there are a lot of empty beds" in existing prisons, Chin said. "So its not clear if a new one is needed."

Alcatraz has "a reputation as a tough prison" and Trump is trying to send a message that his administration will be tough on crime, Chin added.

Former House Speaker Nancy Pelosi, a California Democrat whose district includes Alcatraz, said the proposal was "not a serious one," while the Democratic state senator for San Francisco, Scott Wiener, called the idea "deeply unhinged" in post on Instagram and "an attack on the rule of law."