Mr Wilson was speaking after Ms O’Neill laid a wreath at the Cenotaph in Belfast on Friday to mark the anniversary of the Battle of the Somme.
However, although she became the first senior member of the party to mark the occasion, some unionists criticised her for laying the wreath at a Sinn Fein event two hours before the main ceremony - and accused her of deliberately hijacking the day to promote party political messaging.
Ms O’Neill said, “I hope that today’s attendance and the laying of a wreath is actually a demonstration of someone who wants to work for all in our community”.
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But Mr Wilson said that Ms O’Neill is already claiming to be First Minister, something he said she does not become until elected by the Assembly.
“Secondly, he said, “her record so far shows that she and her party are far from being willing to represent all the people of Northern Ireland, even in the churlish way in which she treated the Somme commemoration; she couldn’t go to the main ceremony and had to do it separately, probably because of the presence of the police and army at it. Again it shows that she is mealy mouthed and hypocritical in claims that she makes.
“The third thing is she can hardly be First Minister for all when she and her party continues to glorify people who engaged in sectarian genocide against the unionist population for 40 years.”
He wouldn’t expect her to attend unionist events but there are national events such as centenary celebrations, which “if she truly meant what she said she would be prepared to attend” he said.
Her party wouldn’t allow a rose bush or a tree to be planted at Stormont for the NI Centenary or the Queen’s Platinum Jubilee, he added.
He also raised her party’s opposition to various Orange parades as another hurdle.
A Sinn Fein party spokesperson responded: “The focus of Sammy Wilson and his party should be on forming an Executive to deal with the rising cost of living and supporting workers and families who are struggling to pay their energy bills and on working with others to end the suffering of people on waiting lists by investing the extra £1 billion needed to start fixing our health service.
“They should stop blocking an Executive from being formed, put the interests of people first and get on with the job they were elected to do almost two months ago.”