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The Interior Department said several other states also were seeking arrangements.

“This is a practical and temporary solution that will lessen the pain for some businesses and communities,” Interior Secretary Sally Jewell said.

Utah’s deal lasts for 10 days, while the Arizona deal for the Grand Canyon lasts seven days.

If the government shutdown, which began Oct. 1, ends before the 10-day period ends, Utah said, the state will be refunded the unused money.

Ms. Jewell told the states that she cannot guarantee reimbursement for money spent during the shutdown and said that will be up to Congress.

Members of Congress have accused the Obama administration of closing down far more federal lands than during the 1995-96 shutdown, and they point to decisions at the U.S. Forest Service and the Fish and Wildlife Service, as well as the parks.

“The Obama administration is taking advantage of every opportunity to make this shutdown as painful as possible,” said House Natural Resources Chairman Doc Hastings, Washington Republican.

He and Oversight and Government Reform Committee Chairman Darrell E. Issa, California Republican, have scheduled a joint hearing for Wednesday to demand answers from the Park Service.

Arizona officials accused the Interior Department of “dragging their feet” in working to reopen the Grand Canyon.

The site is a major economic driver for northern Arizona, particularly in the fall. River outfitters, inns and campgrounds all have said they are taking a serious financial hit with the park closed.

Meanwhile, a preservation group that advocates for wild horses last week accused the Fish and Wildlife Service of recalling furloughed workers and spending tens of thousands of dollars, despite the shutdown, to process horses for sale.

The preservation group said the horses were being shipped to a middleman for a slaughter operation.

But even as it continued to prepare the horses for shipment, the service said, the shutdown forced it to cancel public observation of the captured horses.

The groups went to court last week to seek a judge’s intervention.

Meredith Somers and Andrea Noble contributed to this report.