DUP MP Sammy Wilson has called for Conor Murphy to resign or for his party to sack him.
The DUP has so far stopped short of calling for the Sinn Fein Stormont finance minister to stand down after he apologised for branding IRA murder victim Paul Quinn a criminal almost 13 years ago.
DUP leader Arlene Foster, during a Stormont committee on Wednesday, said the apology was the "right thing to do". However when she was asked if he should no longer be a minister in the Stormont power-sharing Executive, she said it was a matter for Sinn Fein.
DUP MLA Paul Frew called for Mr Murphy's resignation on social media.
"He shouldn’t have time to get his coat," he tweeted late on Wednesday night.
His posts on the matter were retweeted by fellow MLA Jonathan Buckley and Councillor Paul Porter.
"If they (Sinn Fein) have any decency," said Sammy Wilson, "Conor Murphy should be required to resign or be sacked."
The East Antrim MP denied he was going against the party line, saying Arlene Foster was correct to state Mr Murphy's position was ultimately a matter for him and his party.
"And if he continues on, it will make it difficult for Sinn Fein to preach to others about integrity and transparency. It will come back to bite them," he told the Belfast Telegraph.
Asked about his party's position in the Executive should Mr Murphy not resign, he said they had no choice but to share power with Sinn Fein.
"We have to live with them because the law says we have to be in government with Sinn Fein. If we could volunteer to be in government with anyone it would not be with them."
By his own criteria he has fallen short. He needs to admit his mistakes and resignSammy Wilson
He added: "They have preached to everybody to have integrity, respect, transparency from public representatives and ministers.
"Now Conor Murphy has had to apologise but only because of the political pressure he and his party has been under.
"By his own criteria he has fallen short. He needs to admit his mistakes and resign."
Mr Wilson added: "If we are to have a new start, a new decade and a new approach - ensure we can trust the people in government - then if that is the case we all have to abide by the exact same standards."
Paul Quinn, a 21-year-old from Cullyhanna in south Armagh, was beaten to death by a gang of around a dozen men in a farm shed across the border near Castleblayney, Co Monaghan.
The IRA were blamed, but Sinn Fein has long denied republican involvement.
A month after the 2007 murder, Mr Murphy, who was Newry and Armagh MP at the time, claimed Mr Quinn was involved in “smuggling and criminality”.
Mr Murphy apologised on Wednesday for the comments.
The brutal murder of Mr Quinn, and Sinn Fein’s response to it, has become a major issue in the Irish General Election campaign, with rivals claiming it is proof of the party’s continued defence of IRA violence.
Mr Quinn’s parents Breege and Stephen have said Mr Murphy’s apology did not go far enough and have called on him to explicitly state that their son was not a criminal.
Both Sinn Fein's president Mary Lou McDonald and vice president Michelle O'Neill stated Mr Quinn was not a criminal.
The BBC's Stephen Nolan show said it received a comment from the party, stating: "Paul Quinn was not a criminal."
However, when asked if the comments could be attributed to Conor Murphy, the show was told "no".
Asked for a comment, Sinn Fein told the Belfast Telegraph Conor Murphy "unreservedly withdrew his remarks made in the aftermath of Paul Quinn's death and apologised to the family".
Mr Murphy said: "I very much regret comments I made in the aftermath of Paul's murder which have added to the grief felt by the Quinn family.
“I apologise for those remarks and I unreservedly withdraw them.
“Once again I offer to meet the Quinn family at a time and place of their convenience.”
The DUP has also been approached for comment.
The courageous stand of Breege Quinn, not just in the last few days but over the past 13 years, as anyone who has followed her activity on social media will know, is an indictment of a political class and a compliant media who have invested so much in a process which requires victims be ignored in order for it to survive.