Police in the North were on high alert after dissident republicans attempted to murder an officer with a car bomb and a second explosive device was discovered close to a PSNI station.
"If that officer had not checked under his car, we would have been looking at a murder or multiple murders," said Mr Hamilton.
In a separate incident, a viable pipe bomb was found close to the gates of a police station yesterday in the Co Armagh town of Tandragee, near Portadown.
Elderly residents were evacuated from their homes nearby – before being allowed to return after army technical officers had dealt with the object and the security alert had ended.
"Those cowards responsible for this have nothing to offer the people of Northern Ireland for the future," he said.
"Whoever they are or whatever cause they profess to follow, cowardly attacks on police officers, police stations or local communities will not advance their cause one iota."
In Belfast, the booby trap device from the previous day was defused in a controlled explosion by the army.
It was recovered from under the officer's car partially intact and police hope forensic tests on the remains will identify those who made and planted it.
Mr Hamilton said he was linking the attack to "anti-peace" dissident republicans, who have already murdered two police officers.
"We are hopeful that it will provide useful evidence," he said. "The fact that it was discovered and it didn't ignite means that we obviously have a starting point, forensically."
Police have been warning for months that republican militants remain determined to kill members of the security forces.
On November 1, prison officer David Black was shot dead as he drove to work at the high-security Maghaberry prison in Co Antrim.
A group styling itself the "new IRA" claimed that attack.
Less than two weeks later, an under-car booby-trap bomb was found lying on a road in west Belfast. It is believed to have fallen from a soldier's car.
In recent months, police in Belfast and Derry have recovered horizontal mortars capable of piercing the armour of police vehicles and causing multiple fatalities.
During the past year, police have arrested 115 people suspected of dissident republican activity, and 35 have been charged. Sixty-four officers have been forced to leave their homes during the past five years because of intelligence that they were being targeted for potential attack.
The chairman of Northern Ireland's Police Federation said he would be seeking a meeting with PSNI Chief Constable Matt Baggott to discuss officers' personal security and the recruitment of extra staff.
Terry Spence said more needed to be done to ensure officers' safety at home and at work.
Northern Ireland Office Minister Mike Penning said everything Mr Baggott and Stormont Justice Minister David Ford had asked for to combat violent groups had been provided, and he joined Mr Ford in condemning the latest attack.
"Those who are responsible offer nothing except terror and misery," he said.