A statement was read out by a masked man at a 32 County Sovereignty Movement rally in Derry to mark the anniversary of the 1916 Easter Rising.
In the statement the group, which was responsible for the 1998 Omagh bombing, said police officers would be targeted “regardless of their religion, cultural background or motivation”.
The group also said: “The Queen of England is wanted for war crimes in Ireland and is not wanted on Irish soil.”
Just two days ago at the GPO, the head chaplain of the defence forces urged people to honour the memory of the Easter Rising patriots by rejecting terrorism and welcoming Queen Elizabeth to the country.
Monsignor Eoin Thynne made the call at the 1916 commemorations in a clear reference to the murder of PSNI officer Ronan Kerr in Omagh this month and to planned protests against the British monarch’s visit next month.
Leading almost 300 members of the defence forces and a crowd of several thousand dignitaries, guests and onlookers in prayer, Msgr Thynne said: “We pray for the strength and the courage to stand up and speak out as one voice against those who persist in cowardly acts of terrorism and show nothing but contempt for Irish people.
“As the island of a thousand welcomes, may we always show our love for our neighbours and extend a céad míle fáilte to all visitors to our shores. May we realise also we can not expect to make everyone our friend but we can try to make no one our enemy.”
Meanwhile, three men have been charged with terrorism offences after a cache of weapons and ammunition were found in a car in Keady, south Armagh, last Friday.
The weapons and ammunition were “not intended to kill anybody”, Newry Magistrates Court heard.
The police had asked people in the North to be “particularly vigilant” over the Easter holiday period due to a high level of threat from terrorists.
As a result, there were highly visible checkpoints and patrols across the North all weekend. Further PSNI searches uncovered a stash of bomb-making equipment on Saturday.
Also on Saturday, a man was charged in connection with the murder of Constable Ronan Kerr three weeks ago. Gavin Coyle, aged 33, from Culmore Park, Omagh, was charged at Dungannon Magistrate’s Court with possession of explosives, firearms and articles likely to be of use to terrorists. He was remanded in custody for four weeks.