Officers say the device at Holy Cross Church on Crumlin Road was designed to kill but failed to detonate.
The bomb was described by detectives as "advanced and sophisticated" and it is thought it was hurled at a patrol vehicle outside the church at 12.45am.
When it failed to go off, police believe the culprit phoned the parish priest to warn him about the danger.
Rector of the church, Fr Gary Donegan, told Premier the parish priest was told on the phone that there was a device in the church grounds.
He said: "I went out to look myself to check so, in the meantime, if anyone passed before the police arrived I could keep them away from it."
Fr Gary added that the parish was left without emergency contacts until around 10:30am because of the security alert.
He said they were still going to celebrate Mass at 10am, regardless of the situation.
"We were obviously going to go ahead with the Mass behind closed doors, within the church itself.
"Nothing was going to stop us celebrating the Eucharist, but what was going to happen, probably for the first time since we came here in 1869, there was going to be no public present.
"But we managed to be able to get a couple of dozen people in down the side of a wall."
PSNI district commander chief superintendent Nigel Grimshaw said the bomb was attempted murder.
"This was a shameful attack on officers who each day go out to serve this community and keep people safe and must be out rightly condemned.
"Such disruption to community life is totally unacceptable.
"People should not be subjected to such inconvenience and disturbance to their everyday lives, particularly where families with young children, the elderly and vulnerable are forced out into the cold in the early hours of the morning.
"We are thankful this morning that no one has been hurt and we know that the community here are as appalled as we are at this attack on local community police officers by a small number of misguided individuals."
Fr Gary also condemned the attack: "The fact that it's consecrated ground makes it such a violation.
"Basically, we just found it contemptible that anyone would attempt to maim or kill in the vicinity of consecrated ground."