NEW YORK (Reuters) - The Statue of Liberty, shuttered by the federal government shutdown, reopened to visitors on Sunday morning after New York State agreed to give money to the National Park Service to pay its workers to be there.

It was one of 10 other national parks and monuments to reopen this weekend under similar deals with state governments, the National Park Service said, including the Grand Canyon National Park in Arizona.

In New York, Governor Andrew Cuomo said the state will give the federal government $61,600 a day, allowing visitors to take the ferry over to visit the monument on Liberty Island in New York Harbor.

Speaking at a press conference on Sunday near where ferries to the island depart, Cuomo called it an "unusual arrangement", but said that amount it will cost the state "pales in comparison to the amount of money we're losing."

He said the closure of the 305-foot-tall (93-meter-tall) monument, one of New York City's most popular tourist attractions, was costing local businesses money and threatened hundreds of jobs on Liberty Island, nearby Ellis Island and the ferries that run between them and Manhattan.

"When you close down the Statue of Liberty, you close down a good portion of the tourism that comes to New York City and that has been untold millions of dollars in damage," Cuomo said. "So the state of New York said to the federal government, 'If you don't want to open the Statue of Liberty, we will.'"

The statue only recently reopened after damage to the island's infrastructure caused by Superstorm Sandy a year ago forced the National Park Service to close the island for nearly eight months.

Bradford Hill, the president of Evelyn Hill, the company that runs the restaurant and gift shops on the island, said the latest closure had forced him to lay off all of his 110 employees, who would be rehired now the statue was reopened.

"We were heartbroken to do so," he said. "But it's heartening to know that when Washington, D.C., fails to deliver to Americans, and there's no end to the gridlock in sight, we have a state that we can rely on to step up to the plate and take over critical responsibilities."

The state has agreed to fund the next four days, and will then review the arrangement every two days if the shutdown continues, Cuomo said.

In all, 401 National Park Service attractions across the United States were forced to close to visitors on October 1 after the U.S. Congress and the White House failed to reach an agreement on raising the nation's debt limit.

About 280 million people visit the parks and attractions every year.

More than 7 million Americans were kept out of the parks over the first 10 days of the shutdown and $750 million in visitor spending was lost, according to estimates by the Coalition of National Park Service Retirees.

(Reporting By Jonathan Allen; Editing by Scott Malone and L Gevirtz)