Northern Ireland First Minister Peter Robinson said the Queen is not "in the business of doing deals" but he hopes a meeting with Martin McGuinness can be arranged.
The DUP leader was responding to Sinn Fein claims that a "do-able proposition" on a royal handshake had yet to be agreed.
Mr Robinson said: "I don't think Her Majesty is in the business of doing deals on these matters."
But he called on republicans to show respect to the Queen's importance to many people in Northern Ireland when she visits later this month.
"We're not asking Martin McGuinness to become a royalist," he said. "All we're asking for is that there is a recognition of the two traditions that exist in Northern Ireland, and that is something that both he and I have to do."
Mr Robinson said he had met the president of Ireland, had attended a Catholic church, and sat among supporters at a Gaelic football match as part of his efforts to reach out to nationalists.
He said such gestures challenged some of his political support base, but added: "They look so difficult to do on one side of it, but after you've done it, you wonder what the fuss was about."
He noted that the Queen had a family member, Lord Mountbatten, murdered by republicans. "So these are difficult issues and Her Majesty is able to overcome these difficulties. I think Sinn Fein should be able to overcome these difficulties as well."
On her state visit to the Irish Republic last year the Queen laid a wreath to republicans who died fighting British rule. She also broke new ground by speaking Irish during a banquet held in her honour.
There has been widespread speculation that Sinn Fein was negotiating a meeting between the Queen and Martin McGuinness. But last weekend the party said it was surprised by media reports that 10,000 tickets will be handed to the public for a major Diamond Jubilee event at Stormont to coincide with the Queen's visit to Northern Ireland on June 26 and 27. This sparked political tensions around the prospect of a royal meeting with republicans near such a celebration.