The MV Solomon Trader was blown on to a reef off the Rennell Island bay a month ago and it has spilt about 100 tonnes of heavy fuel oil.
Caretaker Prime Minister Rick Hou told media the mining company Bintan Mining Solomon Islands wanted to continue mining and loading incoming vessels.
He said chiefs on the island also wanted their people to continue to work so they can earn money for food.
But Mr Hou said restricting activity on the bay would bring significant benefits to the recovery operation.
