DUP leader Arlene Foster has called on Sinn Fein to specifically condemn the IRA's attempts to kill her father and deputy party leader Nigel Dodds during the Troubles.
There has been an ongoing row over banners being placed around Belfast and further afield attacking Sinn Fein General Election candidate John Finucane.
Sinn Fein had called for the DUP to condemn the material which attacks Mr Finucane and members of his family, including his late father Pat, who was murdered by the UDA in 1989.
"It is a bit rich to listen to people talking about violence and hate crimes and what have you," said Mrs Foster at a DUP policy launch on Tuesday.
"We need complete clarity from Sinn Fein around some of the most violent acts that took place here in Northern Ireland. What do they have to say about the attempted murder of my father (the late John Kelly) for example, what do they have to say about the attempted murder of Nigel Dodds?
"We need to hear from them what they have to say about that."
In response, Sinn Fein accused the DUP of attempting to distract from the issue of the Finucane banners and "anything rather than their reckless Brexit agenda".
Mrs Foster's father, John Kelly a policeman, survived the 1979 attack at the family home. She was eight at the time and had to hide in her bedroom during the terrifying ordeal. He father was badly injured but went on to live for another 32 years. The family were forced to relocate.
Belfast Lord Mayor John Finucane is contesting the North Belfast constituency in a bid to capture the seat held by the DUP's deputy leader Nigel Dodds. Banners have been erected in the past week urging unionists to use their vote.
Nigel Dodds condemned the banners saying they were not part of his re-election campaign and they knew nothing about their origin.
We knew nothing about them and I want to make it very, very clear that anything that is personally abusive or offensive, inaccurate and smearing of any candidate in any political party is to be condemned. North Belfast DUP candidate Nigel Dodds
"It is nothing to do with a proper democratic debate or a democratic election, so I want to make that very, very clear indeed," Mr Dodds said.
An RUC officer was injured after an IRA attempt to kill police officers guarding Mr Dodds while he was visiting his seriously ill child at the west Belfast hospital in December 1996.
Gunmen fired four shots at policemen in a hospital corridor close to where children we being treated. One bullet hit an empty incubator.
The Rev Ian Paisley at the time suggested it was an attempt by the IRA to kill policemen and then assassinate Nigel Dodds.
Mr Dodds added: "Our party has been crystal clear on these issues, on violence and on the use of violence. And the challenge to all parties is the same - we see some vile internet trolling of victims, of unionists politicians as well, and that's to be condemned also."
Sinn Fein MLA Alex Maskey said Mrs Foster and Mr Dodds' comments were a "transparent distraction" from the issue.
“All parties should unite in calling for these banners to be removed and on those responsible to desist. The DUP’s relationship with loyalist paramilitaries exposes entirely their hypocrisy and their selective attitude to violence and sectarianism," he said.
“There is no single and agreed narrative to the past and Sinn Féin is not interested in refighting the battles of the past. Our party has had members killed including our vice-president Máire Drumm who was murdered in her hospital bed.
“There is a responsibility on all political leaders to engage fully in the efforts to build the peace and the process of reconciliation and healing by implementing the mechanisms agreed at Stormont House to support victims and their rights to truth and justice.”
The PSNI confirmed on Monday it received reports about the banners and enquiries were underway to establish if any crime had been committed. Belfast City Council removed one of the banners from a play park on Monday. The PSNI also attended the Tigers Bay play area at the request of the council to ensure the safety of those removing the banner.