PSNI Assistant Chief Constable Will Kerr says detectives are treating the incidents as attempted murder.
He called for the public to remain vigilant, as officers are concerned there may be other devices "out there".
He said: "These devices were designed to kill and designed to kill police officers and we are very lucky we are not dealing with a fatality. Royal Mail staff were also put at risk with these viable devices."
The first letter bomb was found at the postal sorting office in Mallusk, Co Antrim in the early hours of Friday morning after postal workers raised the alarm.
It was addressed to Matt Baggott at police headquarters in Knock in east Belfast.
Army bomb experts were tasked to the scene and made the device safe overnight.
Police have confirmed that a second letter bomb was addressed to a high profile senior serving officer, whose name has not been disclosed, in Londonderry.
An alert, which has now ended, was sparked at Royal Mail premises in Lisburn, Co Antrim on Friday morning after the suspect package was intercepted.
The delivery office on Linenhall Street was evacuated while army bomb experts defused the device.
ACC Will Kerr said dissident republicans are believed to be behind the attacks.
Undoubtedly those dissident groupings wanted to kill police officers.
PSNI ACC Will Kerr
"These groups remain dangerous. They may be small, they lack any political objective, they certainly don't have any support within their own community but they remain dangerous - not just to police officers but to the community at large," ACC Kerr explained.
"Fortunately, we're not dealing with fatalities this morning but we could very easily have been dealing with somebody very seriously hurt or killed," he added.
He said that the Chief Constable and police service would continue "to deliver a policing service to the people of Northern Ireland irrespective of this threat".
It is the latest in a series of incidents targeting PSNI officers, in a week which also saw pipe bomb attacks on police in Newtownabbey and in Londonderry.
ACC Kerr said members of the public should report any suspect activity immediately.
"With two devices this morning, we are concerned there may be others out there so if you have any concerns or suspicions at all, please contact us and we will check it out. We would much rather be safe than take any risk with peoples' lives at all."
Secretary of State Theresa Villiers has condemned those responsible.
"The Police Service of Northern Ireland and the Chief Constable are at the forefront of delivering community policing to keep people safe and secure across all of Northern Ireland," she said.
She added: "They have widespread community support. Those responsible for this device have almost no support and have demonstrated a blatant disregard for the safety of those who could have been injured by this callous and reckless attack."
Ms Villiers said that the Chief Constable undertakes a "challenging role in delivering community policing in a difficult threat environment" and that the PSNI has her full support.
I am certain that the vast majority of people in Northern Ireland will condemn this disgraceful bomb attempt and others which have taken place over recent days.
Secretary of State Theresa Villiers
Justice Minister David Ford said that those responsible for the "senseless attempt to attack the Chief Constable have absolutely no place in a normal society".
The Alliance leader added: "The Chief Constable plays a vital role leading a police service that works right across our community, helping us recover from the dark days and he deserves the support of all.
"Those who sent this device have no concern whatsoever for the staff at the Mallusk Sorting office, whose vigilance is to be commended."
Anne Connolly, the chair of the NI Policing Board, said: "The staff at the sorting office are to be praised for their vigilance in spotting this device but once again there was complete disregard for the serious harm that could have been caused to many.
"The PSNI are working to keep the community safe from harm whilst those responsible for these devices simply don't care who is hurt."
Royal Mail said there are strict procedures and protocols in place to deal with suspect devices and that the safety of all staff is their number one priority.
"There will be a knock-on effect on deliveries and we apologise to customers for the inconvenience this may cause," a statement said on Friday.
Anyone with information in relation to the incidents or anyone who sees any suspicious items or objects is asked to contact police.