Shell confirmed that drill ship Kulluk struck ground near the southeastern shore of Sitkalidak Island on Dec. 31.
Kulluk left Dutch Harbor, Alaska, for prospective drilling sites in arctic waters in August. The company aims to access an offshore region said to have more than 20 million barrels of oil.
Environmentalist groups expressed concern about the potential for damage to the arctic should a spill take place. There were no signs of oil leaking from the grounded drill ship, however.
Shell, in a statement, said the safety of responders was its top priority, adding "severe weather conditions continue to impact operations."
Steve Russell, on-scene response coordinator for the state, said in a statement Wednesday the primary objective was to avoid environmental damage.
"With the Kulluk grounding within state waters, we will closely monitor the recovery of the rig with the goal of little to no environmental impact," he said.
Shell in November said that, after weeks of "safe" and "successful" drilling in arctic waters off Alaska, it concluded its exploratory program for 2012 because of seasonal issues.
In September, it announced it was abandoning parts of its drilling program there after the containment dome designed for a potential oil spill in arctic waters was damaged.