ANCHORAGE — A large floating drill rig that ran aground a week ago on a remote Alaska island arrived as planned Monday in the shelter of a Kodiak Island bay after being towed about 45 miles through swells as high as 15 feet, officials said.

The Royal Dutch Shell PLC vessel was lifted off rocks late Sunday and towed away from the southeast side of Sitkalidak Island, where it sat exposed to the full-on fury of Gulf of Alaska winter storms since grounding near the beach there on New Year’s Eve.

The Kulluk — a circular barge with a diameter as long as nearly three basketball courts — was towed for about 12 hours to the protected waters in Kiliuda Bay, where it will undergo further inspection, including an underwater look at its hull.

“We could not be more impressed with the caliber of the response and recovery crews who were safe and meticulous in their effort to move the Kulluk offshore,” Shell Alaska spokesman Curtis Smith said by email.

The vessel will remain in the bay 43 miles southwest of the city of Kodiak until inspectors review its condition and the Coast Guard clears it to travel. Shell incident commander Sean Crutchfield said there’s no timetable for departure.

“Until we have that damage assessment, we’ll not be able to develop those plans,” Crutchfield said at a news conference Monday.

The massive effort to move and salvage the ship involves more than 730 people, according to the Unified Command, which includes the Coast Guard, Shell and contractors involved in the tow and salvage operation. Eleven people are aboard the ship — a salvage crew of 10 people and one Shell representative

Shell earlier reported superficial damage above the deck and seawater that entered through open hatches. Water has knocked out regular and emergency generators, but portable generators were put on board last week.

The Kulluk is 266 feet in diameter with a derrick in its middle and a funnel-shaped, reinforced steel hull that allows it to operate in ice. Its derrick rises 160 feet. The barge drilled last year in the Beaufort Sea and was headed to Seattle for upgrades and maintenance when it ran into trouble.

Its towing vessel, the 360-foot anchor handler Aiviq, on Dec. 27 lost its line to the Kulluk in heavy seas and hours later lost power to all four of its engines, possibly due to contaminated fuel.

Four reattached lines between the Aiviq or other vessels also broke in stormy weather. The Aiviq on New Year’s Eve again broke its line, leaving the Kulluk attached to the tugboat Alert.

Coast Guard Capt. Paul Mehler, the federal on-scene coordinator, said Monday the Alert also experienced a mechanical problem the night the Kulluk went aground. The agency is investigating.

“The understanding the night of the response was that when she was taking maximum power, there was an engine problem,” Mehler said. “They did recover that within 30 minutes. The details of that, I couldn’t answer yet.”

Inspections after the grounding determined that the Kulluk could be towed, and the Aiviq on Sunday reattached a tow line. Tension was added to test the line Sunday night and increased as high tide approached, Crutchfield said.

He was not on scene but did not hear of complications.

“The Kulluk came off reasonably easy, would be my assessment,” he said.

Mehler said he was in the command center when salvors reported the Kulluk had come off the rocks.

“I won’t say that I saw anyone high-fiving,” Mehler said. “I’ll say there was certainly a sense of relief, but recognizing now we have a lot more work to do.”

Likewise, the tow “has gone pretty much according to plan,” Crutchfield said.

Inspections will involve an underwater look at the hull with divers or remotely operated underwater vehicles or divers or both, he said.

The Kulluk will be tethered to two tugs in the bay and will attempt to set its anchor. If that doesn’t work, he said, additional tugs will be used to keep it in place. Four more tugs were on scene Monday.

A tug trailing the drill vessel used infrared equipment to watch for oil sheens and reported no petroleum discharge.