Sinn Fein's Martin McGuinness meeting with the Queen next week is an effort to reach out to unionists in Northern Ireland, his party leader said.
He told BBC Sunday Politics that the party was "moving beyond rhetoric" and reaching out to unionists as a "gesture of respect".
Although he said he was against the idea of monarchy, Gerry Adams told republicans he wanted to reassure the unionists of their place in his vision of a united Ireland.
The Sinn Fein president said his party was correct to boycott the Queen's historic visit to the Republic of Ireland in 2011, but predicted the encounter planned for Belfast on Wednesday would be a milestone in the peace process.
"This week's meeting is a clear expression of our desire to engage with our unionist neighbours and to demonstrate that we are prepared, once again, to go beyond the rhetoric, as we seek to persuade them that our new Ireland will not be a cold house for unionists or any other section of our people," said Mr Adams.
"Republicans are democrats and the new republic we seek is pluralist - now and in the future.
"It is an Ireland of equals in which there is space for everyone and for all opinions and identities."
He added: "So, Sinn Fein is for a new dispensation in which a citizen can be Irish and unionist.
"Where one can also claim Britishness and be comfortable on this island.
"It is an Ireland which would in a real and inclusive way live up to the ideals of the 1916 Proclamation and cherish all the children of the nation equally."
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The charity Co-operation Ireland is hosting a celebration of culture on the island of Ireland in Belfast's Lyric Theatre and the venue will provide the stage for the first meeting between Sinn Fein and the Queen.
Ireland's head of state, President Michael D Higgins, is also to attend.
The historic handshake is expected to take place in private before the VIP guests join others at the event. But Mr Adams said he has no objection to the handshake being photographed.
Mr Adams confirmed on Friday that his party's ruling executive had agreed to accept the invitation issued to Mr McGuinness, who shares the Office of First Minister and deputy First Minister at Stormont with unionist leader Peter Robinson.
The Sinn Fein leader said the Queen's state visit to the Republic had taken 100 years to be agreed.
He said the Belfast engagement would take place outside of the Queen's Diamond Jubilee celebrations and was being held in the context of the all-Ireland relationships heralded by the 1998 Good Friday peace agreement.
But Mr Adams said the meeting would nevertheless be difficult for nationalists who had suffered state violence during the Troubles.
He added: "The Ard Comhairle decision reflects a confident, dynamic, forward-looking Sinn Fein demonstrating our genuine desire to embrace our unionist neighbours.
"It reflects the equality and parity of esteem arrangements which are now in place.
"It will be another important and necessary step on our collective journey."
The handshake will be viewed as another in a long list of dramatic advances in Anglo-Irish relations.
One of the most significant was the Queen laying a wreath at the Garden of Remembrance in Dublin, which honours republicans who died fighting British rule, followed by a tour of the headquarters of the Gaelic Athletic Association (GAA), before she spoke Irish at a banquet in her honour.
Since those events, Mr McGuinness has spoken several times of how he was struck by the Queen's gestures.
Mr Robinson had said republicans should pay due respect to the Queen as a recognition of her importance to many in Northern Ireland.
The First Minister was also among those who said such a meeting would also be difficult for the Queen, given that her own family was hurt by republican violence when the IRA killed Lord Mountbatten in a 1979 bombing in Co Sligo.
But the Democratic Unionist leader welcomed the planned meeting.
Mr Adams also recognised the gestures made by the Queen in Dublin.
He added: "We have to change Irish society now, north and south, to accommodate the unionist population and their cultural identity.
"The meeting between Martin McGuinness and the Queen will assist in that process of change.
"The people of this island deserve the very best society that can be created.
"I believe this initiative will contribute in a symbolic yet significant way to this necessary work."