It follows the publication of a list of locations with branches deemed at risk of being closed or restructured, and news that up to 1,000 jobs could be affected.
Areas in Northern Ireland set to be impacted include Antrim, Belfast, Derry~Londonderry, and Newtownards.
Ms Mulholland has said: “The closure of any local Post Office branch stands to hit the most vulnerable in society the hardest, and so this news is greatly concerning.
“The local Post Office is often the focal point of any community. Particularly in more rural areas, older people, those who are disabled, those who have caring responsibilities, and those who do not own cars may face near-impossible journeys to reach their local Post Office, and any change to where they can access services will be greatly inconvenient for so many.
“We must make sure these services remain accessible for all that rely on them.”
Ms Armstrong, whose Strangford constituency is due to be impacted by the inclusion of Newtownards in the list of branches at risk, added: “News of these potential closures will be incredibly worrying, both for my own constituents in Newtownards and for many more people right across Northern Ireland.
“The loss of a local Post Office branch will be devastating for some, and see a knock-on effect to other branches in the surrounding area, as well as potentially increasing social exclusion and damaging community cohesion.
“While I recognise that times are tough and efficiencies may need to be made, people depend on these services. I would urge the Post Office to reconsider this decision, but in the meantime, we must ensure the impact dealt to people in affected areas, many of them vulnerable, is softened as much as possible.”