ANCHORAGE — A Royal Dutch Shell drilling vessel pulled from rocks off a remote Alaska island headed to shelter Monday in a protected Kodiak Island bay.

The Kulluk, a circular drill barge without its own propulsion, ran aground New Year’s Eve in a powerful storm. It was being towed to Seattle for maintenance before it ran aground, but the lines that connected it to the towing ship broke.

That same ship, the 360-foot Aiviq, pulled the Kulluk off the rocky bottom near Sitkalidak Island at 10:10 p.m. Sunday and started a slow tow toward Kiliuda Bay.

High winds and sea swells threatened to slow the barge’s 30-mile journey to the bay. But the ship made steady progress, moving about 4 miles per hour. By 9 a.m., the vessels were about four miles from where crews planned to anchor up.

The 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 and one Shell representative.