The first minister has spoken of the difficulties she experienced with the deputy first minister, because of his graveside oration at the funeral of the man who, she believes, tried to kill her father.
IRA gunman Seamus McElwaine was shot dead by the SAS in April 1986.
He was preparing to ambush a British Army patrol near Roslea, Fermanagh.
At his funeral two days later, Martin McGuinness described him as a "highly intelligent volunteer".
Mr McGuinness said McElwaine was a "freedom fighter murdered by a British terrorist".
He went on to say that he was a "saint", when compared to Margaret Thatcher and Ronald Reagan.
Mrs Foster said she believes it was Seamus McElwaine who had attempted to murder her father, John Kelly, in 1979, based on information provided to her family by police.
Speaking to the BBC's Spotlight programme, she said, "It is quite difficult. If you talk to Martin McGuinness now, he will say that unionists aren't the enemy, the enemy is poverty, the enemy is unemployment.
"And that's fine, but it doesn't take away from the fact that he thought it appropriate to speak at Seamus McElwaine's funeral - a man who had been responsible for murdering many people in County Fermanagh."
She added that despite her personal difficulties, she would work with the deputy first minister because: "The past is the past".
"What I want to do is to build a future that everybody in Northern Ireland can ascribe to," she said.
In a statement on Tuesday, Mr McGuinness said: "There will always be more than one narrative to any conflict.
"There is hurt on all sides and all of us - including the media - have a responsibility to recognise that if we are to consolidate peace and build genuine reconciliation.
"That is what I am committed to and I intend to stay positive in that work," the deputy first minister added.
"People like myself, Arlene Foster and all politicians have a huge role to play by giving positive leadership in the work of reconciliation and coming to terms with the past."
This interview can be seen on Spotlight on Tuesday 9 February on BBC One NI at 22:45 GMT