Sinn Féin's Barry McElduff is to stand down as a Westminster MP with immediate effect.
The 51-year-old Sinn Féin member, who is MP for West Tyrone, caused controversy last week after he posted a video showing a loaf of bread with Kingsmill branding on his head.
The video was tweeted on the 42nd anniversary of the shooting dead of ten Protestant workers by republicans at Kingsmill in Co Armagh.
In it he was filmed walking around the shop with the loaf on his head, asking where the store kept the bread.
He said his greatest regret was the "deep and unnecessary hurt" his video had caused the Kingsmill families.
"I again offer my profound apology to those families and to the wider victims community," he added.
"Had I been conscious of the connection to the terrible atrocity at Kingsmill I would certainly not have posted that tweet. I genuinely did not make that connection, not for a second did I make that connection in my mind.
"Kingsmill was wrong, unjustifiable and sectarian. It should never have happened."
Sinn Féin suspended Mr McElduff for three months last Tuesday.
Sinn Féin's Stormont leader Michelle O'Neill said after that meeting Mr McElduff would continue to be paid during his suspension.
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Ms O'Neill said in a statement today: "Yesterday evening, Barry McElduff informed me of his intention to resign as Sinn Féin MP for West Tyrone.
"Barry is doing so as a consequence of the unintended hurt caused to the Kingsmill victims and their loved ones by his recent social media tweet.
"Barry recognises that this controversy and his continuing role in public office is compounding the distress to the victims of Kingsmill, and again offers his profound apology to those families and to the wider victims community.
"He has said that he does not want to be a barrier to reconciliation and I respect that decision."
DUP Leader Arlene Foster MLA said: "It is right that Barry McElduff has resigned. He was not fit for public office and should have resigned in the immediate aftermath of posting the disgraceful video mocking and insulting the horrific terrorist events at Kingsmill.
"Over the course of the last ten days Sinn Féin has failed to deal with the McElduff situation.
"By merely suspending him and continuing to pay him they compounded his disgraceful actions and demonstrated a lack of respect and compassion for the victims of Kingmill and indeed victims more widely.
"Sinn Féin got this badly wrong."
Tánaiste and Minister for Foreign Affairs Simon Coveney said he hoped Mr McElduff's resignation will provide an opening for political leaders in Northern Ireland to take decisions to re-establish the assembly.
Speaking in Cork, Mr Coveney described the resignation as an appropriate response.
He said he had met families of the victims of the Kingsmill massacre, who he described as dignified and sincere people who were seeking the truth.
Fianna Fáil leader Micheál Martin said he believes Mr McElduff took the right decision to resign, given the "enormous hurt" he has caused to families of the victims.
Mr Martin also said he believes Sinn Féin MLA Máirtín Ó Muilleoir should make a more fulsome apology for retweeting the tweet which Mr McElduff uploaded with the loaf of Kingsmill bread on his head.
He described the tweet as despicable, and said questions remained in relation to why Mr Ó Muilleoir had re-tweeted it.
The sole survivor of the attack, Alan Black, was interviewed on RTÉ's Sunday with Miriam, yesterday in which he accused Mr McElduff of celebrating the Kingsmill deaths.
He rejected Mr McElduff's earlier apologies, saying "he done it deliberately to cause hurt and he succeeded in spades in the hurt that he caused".
Mr McElduff said today that he realised many people did not believe his explanation for the video.
"There was no intended reference to Kingsmill in my tweet," he said.
"But I do accept that there are many people who do not believe this to be the case. I accept also that this view of what happened is deeply damaging to the reconciliation process that is so important to consolidating the peace process and to healing the pain and hurt of the past.
"I cannot undo the pain caused but I know that my continuing role as MP for West Tyrone will compound that sense of hurt and impede any reconciliation process."
Mr Black welcomed the resignation.
He said: "This past week has been truly awful for me. I am just hanging by a thread. But I am glad he has done the right thing."
Mr Black said the fallout from the Twitter video forced him to re-live the trauma of the attack in which he was shot 18 times.
"I am going to have to take time now to heal.
"I only got involved because of the hurt and disrespect shown to my friends who died at Kingsmill but this whole thing has taken a heavy toll."
West Tyrone is a safe Sinn Féin seat and the party will likely hold on to it in a by-election triggered by Mr McElduff's resignation.
