Mrs McDonald also appeared to say she was 'sorry' for IRA murders of around 300 Orangemen.
The president of Sinn Fein Mary Lou McDonald has appeared to say sorry for the IRA's murder of around 300 Orangemen during the Troubles and said she would attend the Twelfth of July if she was invited.
In an interview with the News Letter, the new Sinn Fein leader said she was sorry for the "hurt" suffered by members of the Orange Order during the Troubles and said she would go to the Twelfth of July.
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She said: "If I'm invited, yes. I haven't been invited...I will meet everybody, if I could meet every single person, I would meet every single person individually. I have no hang-ups, I want to meet with everybody.
"I had previously said- and I might as well say it through your own good offices- I would very much like to meet the Orange Order. I think it's important."
When put to her the Orange Order has said it will not meet Sinn Fein until it apologises for IRA murders of Orangemen she said: "I think that is so unfortunate."
Asked if she would apologise for IRA murders, she said: "No, look- I have no hang-ups about saying that I am sorry. I am heartily sorry for everybody that got hurt. I am heartily sorry to those who were hurt by the IRA. Of course. Of course."
She added: "Well, that includes the Orange Order. Of course it includes the Orange Order."
Asked by the Newsletter if she would specifically say sorry to the Orange Order and to admit scores of its members had been murdered by the IRA, Mrs McDonald said: "Of course, I am sorry that members of the Orange Order were hurt. Yes. And I'm sorry that anybody was hurt.
She added: “You can play games on these issues. I’ve no interest in that ... that’s not getting us anywhere. I’m sorry that anybody got hurt; I’m sorry the whole bloody... that any of that happened, from start to finish.
“But I don’t think either that it’s a reasonable position for the Orange Order to say ‘well I’m not going to meet with that person because of everything that happened in the past’ because everybody could adopt that position, and then where are we?”
The Belfast Telegraph has approached the Orange Order for comment.