Police are investigating after an MP tweeted a video showing himself with a loaf of Kingsmill bread on his head on the anniversary of the Kingsmill massacre.
Sinn Fein's Barry McElduff apologised and said he never realised or imagined the footage would be linked with the sectarian attack.
Ten Protestants on their way home from work were shot dead on 5 January 1976 in what later became known as the Kingsmill massacre, after the village where it took place.
A 2011 report by a branch of the Northern Ireland police found that members of the Provisional IRA carried out the killings.
On Friday, West Tyrone MP Mr McElduff posted a tweet in which he wrote: "Hey Fred, where do the McCullaghs keep the bread?"
It is believed "McCullaghs" was reference to the shop he was in at the time.
Some accused the MP of making a tasteless reference to the massacre, with a number of unionist politicians calling for him to resign.
On Saturday, Mr McElduff tweeted: "Have deleted video post. Had not realised or imagined for a second any possible link between product brand name and Kingsmill Anniversary.
"Further, I apologise for any hurt or offence caused. Never my intention to offend anyone who has suffered grievously."
Police Service of Northern Ireland superintendent Emma Bond confirmed that officers were looking into the matter.
"Police have received a number of reports of a post on a social media platform, made by a local public representative. Enquiries are ongoing," she said.
Kingsmill shares its name with the south Armagh village that witnessed one of the worst atrocities of the Troubles.
A group of gunmen stopped a van carrying textile workers on their way home and told the only Catholic to leave.
They then lined up the remaining Protestants at the side of the road and opened fire. Only one of the 11 men hit by gunfire survived the attack.
Democratic Unionist Assembly member William Irwin said the timing and product used by Mr McElduff "raises many questions about the motivation behind this video".
He added: "Given Sinn Fein's repeated insensitivity to victims and glorification of terrorists, PIRA victims throughout the United Kingdom have interpreted this video as a calculated and deliberate insult."
TUV leader Jim Allister said: "Sinn Fein's utter contempt for victims is clearly on display here.
"Any talk of equality or human rights from that party is once again exposed as so much cant and hypocrisy."
Ulster Unionist councillor David Taylor added: "Barry McElduff really is beyond contempt and should be truly ashamed of himself for his actions."
Meanwhile, Alliance Party leader Naomi Long tweeted Mr McElduff, saying: "I see you have deleted your video.
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"Will you also explain what on earth you were thinking of, posting this on the anniversary of the Kingsmills Massacre?
"Have you any apology to make to those victims & survivors deeply hurt by your antics whether deliberate or not?"