The attempted murder took place in the Coolnagard area of the Co Tyrone town on Friday.
It is understood a crude but viable pipe bomb failed to explode when it was thrown at the home of the off-duty officer, who fired two shots at masked men.
As investigations into the incident continue, police said it was lucky that no one was killed or injured by the device when it was carried through the residential area.
Superintendent Alwyn Barton said: "It is very fortunate that this device did not explode and that no one was killed or seriously injured.
"Those responsible for this attack carried a potentially lethal device through a residential area before using it to try to kill an officer.
We are very fortunate that no one was killed or seriously injured as this attack put the lives of all those living in the area at serious risk.
"This was not only an attack on a police officer but was an attack on the whole community of Omagh. Those who carried out this attack have shown callous disregard for the safety of the local community and the police officer serving this community."
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.
Police have appealed for anyone who noticed any suspicious activity in the area last Friday or over the past few months to contact them.
Meanwhile the Police Ombudsman has launched an investigation into the officer opening fire.