Faced with hefty operating costs, the foundation building the 9/11 museum at the World Trade Center has decided to charge an admission fee of $20 to $25 when the site opens next year.

The exact cost of the mandatory fee has not yet been decided.

Entry to the memorial plaza with its twin reflecting pools will still be free.

The decision to charge for the underground museum housing relics of the Sept. 11, 2001, terror attacks has been greeted with dismay by some relatives of 9/11 victims.

“People are coming to pay their respects and for different reasons,” said Janice Testa of Valley Stream, whose firefighter brother Henry Miller Jr. died at the twin towers. “It shouldn’t be a place where you go and see works of art. It should more be like a memorial place like a church that there’s no entry fee.”

Testa was visiting the memorial Saturday with relatives from Florida.

The memorial plaza opened in 2011 on the 10th anniversary of the terror attacks, but disputes over funding have pushed the museum’s opening back to spring of 2014.

With the cost of operating the memorial and museum projected to be $60 million a year, the memorial foundation voted at its board meeting last week to charge a mandatory admission fee for the museum.

“This is something that is going to be important and is going to be worth the expenditure,” Joseph Daniels, president of the National September 11 Memorial and Museum, said Saturday.

Daniels said the museum will be free during certain hours every week and will offer student and senior discounts.

Foundation officials had considered an optional donation but rejected the idea.

“We decided that it’s more fiscally prudent to have a straight ticket charge,” Daniels said.

Debra Burlingame, a foundation board member whose brother was the pilot of one of the hijacked planes, said the trade center site is expensive to build on and to protect.

“The World Trade Center site remains a target of interest among terrorists, so the security has to be robust and relentless,” Burlingame said in a phone interview. “There’s a big price tag on that.

“Would we like to be able to say this is free? Absolutely,” Burlingame added. But she called it “irresponsible to hope that year after year we have donations that will cover an expense like security.”

Some visitors to the memorial were divided about charging admission to the museum.

Retired school psychologist Valerie Cericola of Lavalette, N.J., said the entry fee sounded fair.

“You need to keep it open, you need to keep it running,” she said. “It’s an expense.

But Jennifer Reyes, a friend of Cericola’s daughter who has a connection to the trade center site because she was born on Sept. 11, 2001, said the museum should ask for an optional donation.

“I think a donation like $10 would be good,” Jennifer said.

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