A crude, viable pipe bomb type device was discovered during a security operation in the Coolnagard area of the Co Tyrone town on Saturday.
It was found after an incident on Friday when the officer fired two shots at two masked men at the rear of his house.
The Police Federation for Northern Ireland said the device was "hurled into his home", however, it failed to explode.
No one was injured, but the Police Ombudsman has launched an investigation after the officer opened fire.
PSNI have carried out door to door inquiries to try and establish what happened.
A number of homes had to be evacuated on Saturday while searches were carried out in the area.
The policeman, who owns the house, had previously been stationed in Omagh, but had been transferred to another policing district.
It is understood he no longer lives in the house but was carrying out repairs at the time of the attack.
West Tyrone UUP MLA Ross Hussey said he believes republican paramilitaries had been gathering intelligence on him for some time.
"It's my opinion, this police officer was targeted, they knew where he lived and he was their specific target," he said.
"The device that was found at the house was a viable, improvised explosive device. Had it exploded at or near the police officer, it would either have killed him or seriously injured him.
"Had it been found in a back garden and a child picked it up, we'd have been sitting here today talking about the death of a child."
Police have appealed for anyone who noticed any suspicious activity in the area last Friday or over the past few months to contact them.
It has been less than two years since dissident republicans used a bomb to kill a police officer in Omagh.
Constable Ronan Kerr, who was 25, died when a booby-trap device exploded under his car in April 2011.
Sinn Féin Councillor Sean Begley told UTV: "In the recent past, after the murder of Ronan Kerr, we saw [that] the people of Omagh came out on the streets - people from all backgrounds, people from all types of society - and actually sent out a very clear message on behalf of the people of Omagh that this type of activity wasn't acceptable."