Hartlepool Council faces legal bills of up to £1m following the row over the scrapping of so-called "ghost ships".
Four of the ships have been moored in Hartlepool since 2003
Able UK says it will be seeking costs incurred during a planning inquiry.
The Hartlepool-based firm won a contract with the US Government to dismantle up to 13 vessels in 2003, and four arrived later that year.
Environmental and planning concerns prevented work taking place, but in October the council gave conditional approval to revised applications.
However, an ongoing government planning inquiry is yet to deliver its findings with a decision not expected until early next year.
Able UK said Hartlepool Council's initial refusal had financial implications for the company.
Both parties have been given until 26 November to discuss the costs issue.
Martin Kingston, QC, for the company, told the inquiry: "The unreasonable behaviour has incurred costs because it should not have been necessary for the secretary of state to determine the appeals and the council has behaved, in the course of the appeals, in a manner which has incurred unnecessary expense."
James Findlay, for Hartlepool Council, said the local authority would need time to study the costs application.
He said: "Figures of anywhere between half-a-million pounds and £1m have been mentioned and the council would need time to submit a response."