They have written an open letter to patients and staff amid concerns about the future of services at the West Cumberland Hospital in Whitehaven.
Some services have already moved to Carlisle's Cumberland Infirmary, prompting worry among campaign groups.
But the letter said an A&E at Whitehaven was "non-negotiable".
It also said that no changes to services would be made without a public consultation, and hospital bosses were committed to providing "high quality" care.
However, the letter did reveal that by the spring of 2016,  a "clinical strategy" would be published setting out a plan for local services.
In a recent investigation by BBC Inside Out, staff claimed patients were suffering because services had moved - allegations that North Cumbria University Hospitals Trust, which runs the hospital, denied.
The letter to patients said: "We are all fully committed to the continued delivery of the 24 hours a day, seven days a week, accident and emergency service - this is non-negotiable.
"It is also a very significant challenge, and will require all of our organisations to work together to find improved ways of working to solve the operational and workforce problems in the hospital."
It also said there were no plans to make further changes at the hospital until a review had been carried out.
Some medics spoke anonymously to the BBC's Inside Out North East & Cumbria earlier this month and claimed that "patients have died because of the changes".
Health leaders have insisted they are "fully committed" to keeping open a 24-hour A&E department at a hospital in north Cumbria.