The DUP is due to meet the PSNI chief constable Matt Baggott later to discuss the "escalation" in dissident republican activity.
On Tuesday, a booby-trap bomb partially exploded under the car of a civilian security worker in Cookstown
It was the third attempted car bombing on security personnel in seven days.
DUP MLA Alastair Ross said the party would be seeking assurances the PSNI was "up to the task" of defeating "republican terrorist micro-groups".
"It has been a result of pure chance that members of the police and public have not been murdered by these dissident republican criminal gangs," he said.
"People in the police and wider community are rightly concerned that it is only a matter of time before these murderers succeed in achieving their evil aims and kill innocent people.
"The DUP will continue to lobby for the police to be given the maximum amount of resources to tackle this threat and we will fight to ensure that any measures needed by the police are introduced without delay."
Mr Ross will be joined by fellow DUP policing board members Jimmy Spratt, Jonathan Bell and Ian McCrea at the meeting as well as MPs Gregory Campbell and Arlene Foster.