NuGen, which is overseeing the planned Moorside plant, was initially co-owned by French firm Engie and Toshiba.
Last month the Japanese technology giant announced it was taking 100% control and that has led to NuGen announcing the pause.
Copeland mayor Mike Starkie said he was "sure" the plant would be built.
The Â£10m scheme, near Sellafield, has been dogged by uncertainty as it was rumoured Toshiba would withdraw from all nuclear operations outside Japan due to multibillion-dollar losses.
'Crucial for jobs'
Additionally, its US subsidiary Westinghouse, which is set to provide the reactors, is under bankruptcy protection.
In a statement, NuGen said it was "undertaking a strategic review of its options following shareholder and vendor challenges".
The firm said: "The Moorside project remains a key infrastructure project focused on creating employment and economic prosperity in Cumbria and across the North."
Mr Starkie described the project as "crucial" to creating jobs in the area.
He said: "I am reassured that the reasoning behind the strategic review is to ensure the project is on the right track and the commitment to its delivery assured."
A plan to build a nuclear power station in Cumbria has been put on hold while the company behind it carries out a strategic review.