Officers in Northumbria are searching for Raoul Thomas Moat, 37, who is suspected of critically injuring his former partner, killing her boyfriend, and wounding a police officer.
He was released from prison on Thursday after serving a short sentence for assault and police today appealed to him directly to get in contact.
At a press conference in North Tyneside Detective Chief Superintendent Neil Adamson told Moat: "This must stop now."
Police also named the man shot dead as Chris Brown, 29, who recently moved from Slough in Berkshire to the Gateshead area to take up a job as a karate instructor.
Moat's former partner, Samantha Stobbart, 22, is currently in a critical condition in hospital after the attack in Birtley, Gateshead, in the early hours of yesterday.
It is thought Miss Stobbart was inside a house in the Scafell area when she was shot through the living room window.
Moments later Mr Brown is believed to have left the house, only to be struck down around 50 metres from the front door.
Less than 24 hours later, a man detectives identified as Moat was linked to the shooting in East Denton, Newcastle, in which 42-year-old Pc David Rathband was seriously hurt after suffering gunshot wounds to the face and chest area.
Police said Pc Rathband, married with two children and with 10 years on the force, was carrying out a "static patrol" on a roundabout when he was attacked.
He is in a "critical but stable" condition at Newcastle General Hospital, officers said.
Speaking at the conference today, Mr Adamson said Moat had made contact with the police around the time of the third shooting.
Appealing to Moat, he said: "Yesterday you contacted the police and it is clear that you believe certain things to be true which I would like to clarify with you now.
"You have told us that the police are not taking you seriously. We are. I want you to know that you have our full attention, innocent people have been hurt. This must stop now.
"You believe that Sam was having an affair with a Northumbria Police officer. Sam has told us this is not true. Our inquiries have verified this."
He said he knew Moat was concerned for the future well-being of his three children.
"For their sake, this has to stop now," he said.
"These are not the memories that your children need to have of their father.
"Enough people have been hurt. You need to make contact with us now."
Temporary Chief Constable Sue Sim said that despite being seriously injured, Pc Rathband had managed to provide colleagues with extremely valuable information, "demonstrating his absolute professionalism in the most extreme circumstances".
Many neighbours close to the scene of the shootings in Birtley reported hearing gunshots in the early hours of yesterday and some saw Mr Brown lying on a grassy area outside opposite the house that had been targeted.
Both he and Miss Stobbart were injured by a "shotgun-type weapon", Mr Adamson said.
He also said Moat was released from an 18-week prison sentence for assault but added this was not against Miss Stobbart.
Her half-sister Kelly Stobbart told the News of the World that family members were warned she may not survive.
"We don't think she'll make it," the 27-year-old said. "She's been shot in the chest and stomach, her body's been ripped apart.
"She is on a life-support machine and is critical. The hospital have told us to expect the worst."
Lee Burdis, Miss Stobbart's half brother, said he hoped she would pull through and said he had met Moat quite often during his six year on-off relationship with Miss Stobbart.
"We were actually quite close," he said, "well, I wouldn't say we had close ties but we saw each other a few times.
"He seemed alright at the time but he was a big lad and he does look quite dangerous and could be quite dangerous.
"He's a big lad and he's got a violent past. I know that for a fact because he's threatened to take me round the back of a car before."
Mr Adamson said he felt "anxious" given Moat's behaviour to date.
"There are potential issues for the force, and we are dealing with those as we speak," he said.
There was appropriate risk assessment and strategies in place to deal with any perceived risk.
Ms Sim said all the force's armed officers were deployed on the case, and firearms officers were coming to support from other forces as well.
She said Pc Rathband's family were at his bedside.
Mr Adamson urged anyone who could help the inquiry to call 03456 043043 or Crimestoppers on 0800 555111.
A police spokeswoman confirmed tonight that Pc Rathband had been shot through the passenger window of his police car.
Police also released a new photo - taken in April - of Moat, who is from the Fenham area of Newcastle.
They described him as 6ft 3in tall, white, of large muscular build, with very short or shaven blonde hair and blue eyes.
A Northumbria Police spokesman said: "Anyone who has any information about this man is asked to call police immediately. He should not be approached."