A viable pipe bomb was discovered in the Milltown area of Dungannon at the weekend.
A number of residents were evacuated from their homes in the Mark Street area of the town for several hours on Saturday as police and Army explosive experts took steps to make the device safe.
Residents have since returned home and detectives in Dungannon are appealing for anyone with information to get in touch.
DUP MLA Lord Morrow said those involved in planting the device had no regard for the safety of others.
"I utterly condemn and deplore the actions of those who left a pipe bomb in the Milltown area of Dungannon on Saturday," the Dungannon town councillor said.
"Those involved displayed absolutely no concern for the safety of residents who had to be evacuated from their homes whilst security forces dealt with what transpired to be a viable device.
"This was done to create the maximum inconvenience in the area whilst holding a community to ransom."
Lord Morrow said there had been an upsurge in this kind of activity in Dungannon and added that Sinn Fein's Gerry Kelly was wrong to suggest talking to the people behind the attacks.
"Those behind it need to be brought before the courts," the DUP man added.
"I completely refute Gerry Kelly's suggestion that dialogue with terrorist thugs will bring about a change in mindset, whilst their criminal deeds are conveniently swept under the carpet.
"A cosy chat with disillusioned, dangerous republicans is neither justice nor deterrent. Mr Kelly would serve his community better if he endorsed calls for such terrorists to be brought before the courts and taken out of society. He should be urging his community to give their full support to the police."
Lord Morrow said it was "totally unacceptable" that innocent residents in Milltown should be subjected to the inconvenience of being evacuated from their homes and they were "sick, sore and tired" of this type behaviour.
Ulster Unionist leader Tom Elliott also condemned the attack.
"There is no place in society for such items as pipe bombs," he said. "It is vital that people desist from using these devices. It is also important that the public report anything suspicious to the police.
"I trust the people of Dungannon and surrounding area will remain calm and look out for their neighbours."