Unified Command spokesman Ignacio Gonzalez says the Royal Dutch Shell's Kulluk was attached to the towing vessel Aiviq about 4 p.m. Sunday.
Gonzalez, a Shell employee, says the tow line's tension is being tested on the drill ship grounded off Sitkalidak Island. Crews are waiting for the go-ahead from a salvage team before trying to tow the ship 30 miles to shelter in Kodiak Island's Kiliuda Bay.
Gonzalez says a decision has not yet been made on when the attempt will occur.
Responders say there's no sign the hull of the Kulluk has been breached or that oil has spilled from the vessel.