The NI Secretary of State, Owen Paterson, has refused to confirm or deny whether there has been contact between the government and dissident republicans.
Mr Paterson was speaking for the first time since Martin McGuinness claimed earlier this month the government had been talking to the terrorists.
He told the BBC the government never discussed "operational issues", but said it could not have "meaningful talks" with the groups.
""Our position is completely clear, and consistent with previous governments, you cannot have meaningful talks, serious discussions, real negotiations whatever you want to call them with people who are not absolutely commited to peaceful means of pursuing their goals," he said.
Mr Paterson was talking to Radio Four's Today programme following last weekend's no-warning bomb in Lurgan, County Armagh, which was blamed on dissident republicans and injured three children.
Police later came under attack from petrol bombs and other missiles.
Mr Paterson added:"There are a small number of very dangerous groups and we do not underestimate the threat they pose to the public.
"There are attacks that have failed thankfully in the last week which if they had succeeded would almost certainly have wounded people very badly and possibly could have killed a number of individuals some as young as 12, one as young as two.
"These attacks are disgusting, they will not achieve anything.
"Political violence does not achieve its aims."
DUP East Londonderry MP Gregory Campbell said his party would be meeting with Mr Paterson to seek clarification of his comments.
"We will be meeting with the Secretary of State for Northern Ireland to try and flush this out once and for all," he said.
"This is not too difficult to understand either talks have taken place or they haven't.
"They have either taken place with the approval or the knowledge of the British government, with or without a third party, there are yes or no answers to all of those questions.
"It would be much better if he spelt this out clearly."
There have been a number of bomb attacks on security forces by dissident republican terrorists this month, including a 200lb device which exploded outside Strand Road police station in Londonderry.
Dissidents are also believed to have been responsible for leaving booby-trap bombs under the cars of a soldier, policewoman and civilian police station guard in Bangor, Kilkeel and Cookstown.
On Sunday, PSNI Chief Constable Matt Baggott said he did not think it would be a betrayal if politicians engaged in dialogue with dissident groups, but said conditions would have to be attached.