The PSNI chief said he was concerned by the increasing pace of dissident activity.
It follows the discovery of a mortar bomb near a police station in Strabane and a bomb fitted with a command wire in Derry.
Mr Byrne also reiterated a call for the recruitment of more police officers.
Police blamed both attacks on the dissident republican group the New IRA.
Speaking on BBC Radio Ulster, Mr Byrne said recent attacks were “a departure from what we have seen recently”.He added that he was concerned by “the engineering behind a range of different devices”.
“There are a range of tactics being deployed by terrorists in different parts of Northern Ireland with one sole purpose, that is to kill or seriously injure one of our staff,” he said,
“I think it is a worrying departure in terms of the determination, the tempo and the motivation of people to clearly kill or seriously injure one of our officers.”
Mr Byrne said the PSNI needed another 800 officers to take the total size of the force to 7,500.
This was the level envisaged by the Patten Report in 1999 which led to the creation of the PSNI.
He said: “I am worried that the valiant efforts of officers cannot continue at this rate without support from the government to increase the number of people that I can deploy to communities to fight terrorism.
“I actually think that communities are our biggest weapon in turning round this problem, but to encourage and enable them we need to increase our neighbourhood policing teams right across Northern Ireland.”
The most recent attempt to murder police was foiled in Derry on Monday when a bomb containing commercial explosives was found following a major security search in Creggan.
Police said the New IRA planned to fire the bomb into Strabane police station from Church View, which overlooks it.
Local people said children could have been killed if they had have picked up the device which was left on a wall near homes.