Dissident republican activity in Northern Ireland cannot be dealt with by policing alone, PSNI Chief Constable Matt Baggott has said.
He told RTE he did not think it a betrayal if politicians engaged in dialogue with such groups, but he said conditions would have to be attached.
Mr Baggott was speaking after a bomb attack in Lurgan on Saturday, which injured three children, and subsequent attacks on police.
He said the dissidents were ruthless.
They were prepared to target young mothers who wear the PSNI uniform but they would not succeed in their violent ways, he added.
The children - two aged 12 and one aged two - suffered cuts and shock when a no-warning bomb went off in North Street.
Police investigating other bomb alerts in the town on Saturday night were attacked with petrol bombs and other missiles.
The first and deputy first ministers for Northern Ireland said the violence was disgusting.
First Minister Peter Robinson said: "The bomb attack was designed to maim, injure and kill whoever happened to be close by, including children.
"There can be no doubt as to just how depraved and evil these criminals are."
Deputy First Minister Martin McGuinness said: "No cause or belief will be served by attacks on our children.
"These attacks must stop and stop now, this is not the way forward for any section of our society."
Mr McGuinness claimed on Thursday that the British government has talked to dissident republicans in recent weeks. NI Secretary of State Owen Paterson has denied the government wanted discussions with dissidents.
The bomb went off in a bin on Saturday as police investigated reports of a device left at the Model Primary school in Lurgan.
It exploded at a junction where police would have been expected to put up a cordon around the school. The explosion injured the children after it blew a hole in a metal fence.
Three other alerts in the town were declared elaborate hoaxes.
Chief Inspector Sam Cordner said it was "an absolute miracle" that the children were not more seriously injured by what he called a "sickening attack".
He said the fact that an object was said to have been left in one area, then a bomb exploded in a different place "had similarities to the (1998) Omagh bombing that we would not like to repeat".
"This no-warning explosion occurred in North Street in Lurgan and was an obvious attempt to kill police or injure police officers providing a service to this community as they responded to a neighbouring area following a very vague warning that a device had been left at a local school," he said.
He also condemned the attacks on his officers who he said had suffered a sustained attack with petrol bombs and other missiles.
Chief Inspector Cordner called on "all right-minded members of the community to help the PSNI in bringing these criminals to justice".
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.
SDLP assembly member Dolores Kelly said the violence was despicable.
"I think that like the majority of people in the town, I am absolutely disgusted at this despicable and diabolical act, we are just grateful this morning that there weren't people killed or more seriously injured.
"Certainly those who placed the devices and caused the difficulties last night that was their intent."