Sinn Fein MP Barry McElduff has been summoned to meet his party's leadership to explain a video showing him with a Kingsmill loaf on his head on the anniversary of the Kingsmill massacre.
The West Tyrone MP posted the footage in a tweet which read: "Hey Fred, where do the McCullaghs keep the bread?"
It is believed "McCullaghs" was reference to the shop he was in at the time.
The post, which is being examined by police, prompted calls for Mr McElduff to resign from many who saw it as a tasteless reference to the sectarian massacre.
On Sunday evening, a Sinn Fein spokesman said: "The party leadership will be meeting with Barry McElduff tomorrow."
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 Saturday, Mr McElduff deleted his video and tweeted: "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."
He later offered to meet relatives of the attack but a number of them, including the only survivor, Alan Black, rejected the invitation.
"It was like a punch to the stomach, it was so callous," Mr Black told the BBC. "To mock the dead and dance on their graves is depraved.
"It was designed, in my mind, it was designed to cause maximum hurt and it's done its job in spades."
DUP MP Emma Little Pengelly called on Sinn Fein to condemn Mr McElduff's "crass" post.
"This is a test of the Sinn Fein leadership's commitment to 'respect, honesty and integrity'," she said.
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"The party's West Tyrone MP posted a grossly offensive video. People across these islands have condemned the video mocking the Kingsmill massacre.
"He should hang his head in shame."