The new director of the federal Bureau of Prisons said the agency will "vigorously" pursue "all avenues to support and implement" the president's agenda after President Donald Trump said he was wanted to reopen Alcatraz as a "substantially enlarged and rebuilt" prison.

Over the weekend, Trump posted on Truth Social that he was directing the Bureau of Prisons, along with the Department of Justice, FBI and DHS to reopen the facility.

"The Bureau of Prisons (BOP) will vigorously pursue all avenues to support and implement the President's agenda," said BOP Director William K. Marshall III, who was sworn in last month. "I have ordered an immediate assessment to determine our needs and the next steps. USP Alcatraz has a rich history. We look forward to restoring this powerful symbol of law, order, and justice. We will be actively working with our law enforcement and other federal partners to reinstate this very important mission.

"Just an idea I had,” Trump told reporters Sunday night when asked what prompted his proposal. “And I guess because so many of these radicalized judges, they want to have trials for every single, think of it, every single person that's in our country illegally, they came in illegally. That would mean millions of trials, and it's just so ridiculous what's happening."

Alcatraz, which sits in the middle of San Francisco Bay, has not been an operational prison since 1963, according to the National Park Service, which has maintained it as part of the Golden Gate National Recreation Area since 1972. More than 1 million people visit the island each year, according to the BOP.

The facility, which was built as a fort to protect San Francisco Bay then converted to an Army prison before holding federal inmates, has housed notorious prisoners such as mobster Al Capone. Known as "The Rock," the prison held on average 260 to 275 people, according to the Bureau of Prisons, and many inmates considered the living conditions at the prison to be better than most at the time, the agency says.

It was estimated that it would take $3 million to $5 million for restoration and maintenance work to keep the prison open in addition to daily operating costs, which were far higher than other federal prisons. Alcatraz's daily per capita cost in 1959 was $10.10 compared to $3.00 for the federal prison in Atlanta.

A recent inspector general report estimated that the Bureau of Prisons facilities across the country needed $2 billion worth of repairs. The BOP has had to close facilities because of the dire conditions inside some prisons.

Elizabeth Neumann, a former DHS deputy chief of staff, told ABC News Live that the BOP "already has some pretty significant problems with its existing prisons."

"They've closed a number in recent years just because they can't maintain them. So to try to also turn around something that hasn't been operational for 60 years, and make it habitable for people to be imprisoned would be a lot of money," she said.

And it's not just the cost of getting the facility ready to house inmates, she said.

"San Francisco is a very high cost of living area. Federal employees get paid more if they work in those high cost areas. So it's not really a cost effective solution," Neumann said. "If you're looking to build producer capacity, you would it's more effective to just build something new in a part of the country where the cost of living is lower."

Neumann said she wasn't surprised by Trump's suggestion. She said during his first administration, she was often tasked with researching some of his proposals.

"He has a lot of ideas. People will go off and study them, then they'll come back with the facts and, and usually it gets dropped at that stage," she said.

House Speaker Emerita Nancy Pelosi, who represents the area in Congress, shot down Trump's proposal.

"Alcatraz closed as a federal penitentiary more than sixty years ago. It is now a very popular national park and major tourist attraction. The President’s proposal is not a serious one," she posted on X.