Simon Byrne, who succeeded George Hamilton as PSNI head in July this year, posted the image of himself and four other uniformed officers outside the perimeter fence of Crossmaglen station on December 25.
Two were posing for the picture carrying semi-automatic rifles fitted with large night vision sights.
Mr Byrne’s accompanying tweet said: “On Christmas morning great to meet the team policing Crossmaglen @PSNINMDown. I take my hat off to colleagues policing such a unique part of @PoliceServiceNI. Their sense of duty & optimism is inspiring. Stay safe and thank you.”
The chief constable’s message was later described by SDLP councillor Pete Byrne as an apparent attempt to “set Crossmaglen and south Armagh as a place apart,” while Sinn Fein’s Conor Murphy branded the picture “utterly unacceptable”.
Councillor Byrne said: “While many families across South Armagh were waking up, opening presents and enjoying their Christmas morning, they were hurt and offended to see a Twitter post from the PSNI Chief Constable, featuring officers with heavy weaponry on show.
“A lot of work has been done in recent years to build community relations with the PSNI locally.”
He said he would be seeking an urgent meeting the PSNI boss, and added: “While we all appreciate police officers and other emergency services working on Christmas Day, questions must be asked about the nature of this post. Language and images like this flies in the face of the positive work that has been achieved.”
Mr Murphy said: “The heavily armed officers posing with the chief constable is reflective of the militaristic style of policing that the community in south Armagh has had to endure in recent years.
“This community is no different to any other, any attempt to differentiate the style of policing has not and will not be tolerated.
“As new chief constable, Simon Byrne should have sought to address issues which have eroded the local community’s confidence in the PSNI in south Armagh, but this escapade has shown an intention to do anything but.”
He added: “We need a new chapter for policing in south Armagh.”
A PSNI spokesman said the chief constable “is happy to meet with any community or political representative who has a positive contribution to make about local policing matters”.
The chief constable also faced a strong backlash on Twitter, including criticism from Stephen Travers who survived the 1975 Miami Showband murders.
Mr Travers tweeted: “It is difficult to imagine a more ill-judged Christmas message than this.”
Former senior RUC officer Jim Gamble said he had “liked and retweeted” the image but, on reflection, said it “sends the wrong message about Crossmaglen today”.