Police and political representatives have called on republican dissident groups to stop their campaign of sporadic attacks.
The demands follow a no-warning pipe bomb attack on the PSNI station in Strabane, Co Tyrone, in which the home of an elderly woman was damaged and her grandchildren narrowly escaped injury. Several families had to leave their homes for a time.
The three children, aged between four and seven years, were playing outside the house at Courtrai Park in the town at the time of the attack some time after 9pm on Thursday.
The device launched against the station exploded in mid-air, showering the home of 78-year-old Patsy Devine with shrapnel and causing some damage to the roof.
Mrs Devine was in the company of her two daughters at her home, which backs on to the PSNI station. A high fence separates the two properties.
"I think it's all terrible," she said. "What's it all for anyway? There are only old people up here . . . I was pure shaken. My legs went like jelly on me."
She said the incident was shocking, while the PSNI said it was only by chance that no-one was hurt or killed.
Phil Marks, the local PSNI chief inspector, said: "We are all trying to move forward together, but these people are quite incapable of joining us. It is a very small minority within the community and they are becoming more and more ostracised."
Sinn Féin condemned the attacks and called on the group responsible to end its campaign.
Local councillor Brian McMahon said dissidents had no support and those responsible for the PSNI station attack should "wake up to that".
"There's no support in the community for this grouping and they should stop right away," he said.
Mrs Devine's two sons, Michael (22) and David (17), were part of an IRA group who were shot dead by the SAS in the town in February 1985 as they approached an arms dump which was being staked out by the British army. A third IRA member, Charles Breslin (20), was also shot dead.
West Tyrone has seen a spate of attacks linked to dissident republicans. The most recent was reported to the PSNI yesterday, but officers said the identification of the area, said to be between Mallymagorry and Magheramason near Strabane, was too vague.
It warned the public to be alert for anything suspicious and not to touch any object they think could be linked to an attack.