Staff have gathered to demonstrate outside BBC Radio Foyle after it was announced up to 40 jobs could be cut in Northern Ireland, as part of a drive to save money.
On Wednesday people gathered outside the studios in Londonderry to object to the proposed cuts.
Meanwhile, Foyle MP Colum Eastwood told the Prime Minister cuts to programming and staffing levels will leave the station "totally unsustainable."
Speaking in the Commons, Mr Eastwood said: "The BBC Charter places an obligation on that organisation to allow audiences to fully engage on local issues.
"This decision, in my view, is a very clear breach of that obligation, leaving licence fee payers outside the greater Belfast area without local programming.
"Will the Prime Minister act to defend this very important local public broadcasting service?"
Mr Sunak replied: "I believe very strongly in local public broadcasting and indeed the government has taken steps to support local media.
"I would be very happy to look at the specific issue he raises and bring it up with the BBC."
The changes, announced by BBC NI interim director Adam Smyth, will see the end of Radio Foyle's Breakfast programme and the Inside Business programme on Radio Ulster.
The corporation said it was setting out its plans to "facilitate the enhancement of its digital video and online services and the savings that it will need to make over the coming period".
It said that local investment in BBC iPlayer will be increased, but there will also be output and staffing reductions in news, audio and related areas.
Mr Smyth said: "These are challenging times and we face some difficult choices, none of which are easy.
"We have to find monies to maintain and develop our local presence on BBC iPlayer and to absorb cost pressures across different aspects of our work.
"Our concern in all of this will be to safeguard audience value and benefit and to remain mindful of the impact that this announcement will have on BBC staff in Northern Ireland."
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