The Real IRA has threatened to "execute" police officers and warned that the Queen's first visit to the Republic of Ireland is an "insult".
But the dissident republican group behind the latest threat to police officers in Northern Ireland was criticised for being "morally and politically bankrupt".
A statement from the terrorist group was read by a masked man on Monday in a Londonderry cemetery at a rally organised by the 32 County Sovereignty Movement to mark the anniversary of the 1916 Easter Rising.
It comes as security forces face a heightened threat after the recent murder of Catholic Constable Ronan Kerr, 25, in a booby-trap bomb under his car in Omagh, Co Tyrone.
In a statement, the masked member of the Real IRA said: "Oglaigh na hEireann (the IRA) urge all self-respecting Irishmen and women to resist the upcoming insult that is the visit of a British monarch to Irish soil, the criminal free state government invite is not on behalf of the Irish people but to further the selfish interests of a self-serving elite.
"Despite the best efforts of the media, big business, and other power blocks to portray this visit as acceptable we clearly state that the Irish people will not capitulate. The Queen of England is wanted for war crimes in Ireland and not wanted on Irish soil. We will do our best to ensure she and the gombeen class that act as her cheerleaders get that message."
The Real IRA said police officers would be targeted "regardless of their religion, cultural background or motivation".
Foyle MP Mark Durkan said their pretensions to legitimacy would impress nobody. Former SDLP leader Mr Durkan said: "The Real IRA's words are intended to intimidate everyone but their pretensions to legitimacy will impress no one. Politicians do not really have to argue that this group is morally and politically bankrupt when they are driven to attack and threaten nationalists who want to serve the community and their country through a policing vocation. Their statement speaks for itself."
Amid the violence, the Queen's forthcoming visit to Dublin is an effort to strengthen ties between the two countries. Irish president Mary McAleese extended the invitation.
This month motorists near Newry, Co Down, close to the border with the Irish Republic, drove past a car bomb when they moved cones placed there by police.