The Prince George’s County Council on Tuesday unanimously approved a plan to spend millions of dollars to help cover Dimensions Healthcare System’s debt, as the company readies its application to state regulators for a $645 million regional hospital.

The proposal from County Executive Rushern L. Baker III (D) would allocate $5 million annually, for at least five years, to cover interest payments for Dimensions’s bonds, and is aimed at helping convince state regulators that the project is financially sound.

The vote came as Dimensions expects by week’s end to submit its application for the new hospital. The county’ financing plan would redirect $5 million of $15 million annually the county already spends on the current hospital system. Officials have said that they expect that when the new hospital opens, many of Dimensions’s financial problems likely would disappear.

Dimensions — a not-for-profit organization that operates Prince George’s Hospital Center and three other sites in Prince George’s — is also taking steps to reduce its $74 million pension liability.

The new 259-bed hospital, expected to open by 2017, would operate as part of the University of Maryland Medical System. The medical system had said Dimensions needed to shore up its finances before it would agree to the deal.