Mr Wheelhouse also passed on his condolences to the family of a crewman killed when an oil support vessel was hit by severe gales.
BBC: Gales and high tides cause damage across eastern Scotland
An oil supply vessel, Olympic Zeus, has sailed to the scene.
The oil drilling vessel, which has no engines of its own, was being towed for maintenance when it ran aground during a powerful storm on New Year's Eve.
Two helicopter crewmen have been honoured for their role in a North Sea rescue after an oil industry supply vessel was hit by a wave during storms.
Ian Clayton from the RNLI said there were concerns about possible environmental damage if oil started leaking from the vessel.
Officials said that so far there's no sign the hull of the Kulluk has been breached or that oil has spilled from the vessel.
Mr Clayton said there were concerns about possible environmental damage if oil started leaking from the vessel, but there have been no reports of any leaks.
It is believed the oil came from a ship, but the vessel has not yet been identified.
Mario Ploner, the managing director of Tecnomeccanica Biellese, says the ship-based system will use external booms running parallel with the vessel's sides to channel oil onto wool that has been spread over the surface of the sea.
These algae now release their oil, which floats to the surface of the culture vessel.
The supply vessel was carrying 45, 000 litres of red diesel and 78, 000 litres of lubricating oil on board.
The vessel was carrying nearly three times its recommended limit of 74 passengers, including many indigenous tribal palm oil and timber workers returning to their home villages for a harvest festival holiday, said Bakar Sibau, a district police chief in Malaysia's Sarawak state.
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