A man and woman were injured in the attack in the Chippendale Avenue area of Bangor.
Both were taken to hospital. The PSNI initially said one was critically injured.
The suspect, who was armed with a hammer and a knife, remained at large on Christmas Day, with the public being warned not to approach him.
The PSNI released an image of the suspect this evening, as they made a fresh appeal for information.
One local councillor said there was a sense of fear in the area.
Independent Unionist Wesley Irvine, who lives near the scene, said the incident had changed the mood in the area on Christmas Day.
“It stokes a bit of fear among people and people are wary about rapping doors until such time as they can apprehend him,” he said.
“On Christmas Day there are a lot of people travelling from house to house to see family and friends and there is certainly some fear about.
“It certainly came as a big surprise, I live not far from Chippendale Avenue, it’s a quiet residential area of established family homes and people would be long established in the area.”
Mr Irvine added: “It certainly came as a big shock and not the sort of thing you would think would happen in that area.”
Police remained at the scene on Christmas Day, carrying out enquiries.
The Belfast Telegraph understands officers from the Armed Response Unit attended the incident.
Officers with firearms drawn could be seen searching the area.
Police investigating a report of a stabbing in the Chippendale Avenue area of Bangor have released an image of the suspect.
Police at the scene of double stabbing incident in Bangor
The air ambulance also attended the scene.
In an update on Thursday, Chief Inspector Rocks said the suspect remained at large.
“At approximately 3.30pm yesterday, Wednesday, police received and responded to a report that a man, who was armed with a hammer and a knife, had entered a residential property and assaulted a woman aged in her 50s and a man aged in his 20s, before leaving the scene on foot, still armed,” the officer said
“They were both taken to hospital for treatment for their injuries.
“An investigation is underway, and efforts are being made to locate the suspect, who is described as being approximately 5ft 10 ins in height, with short, dark hair, and wearing a blue hoodie, a grey coat, a dark coloured t-shirt, blue jeans, and dark trainers with white soles.
“We are urging members of the public not to approach him if they see him, but to create a safe distance and contact police immediately on 101, and quote reference number 914 of 24/12/25.
“You can also submit a report or information online using the non-emergency reporting form via www.psni.police.uk/makeareport, or contact Crimestoppers anonymously on 0800 555 111 or online at www.crimestoppers-uk.org/.”
Local DUP councillor Alistair Cathcart said: “I wish a full recovery to the two people taken to hospital following a multiple stabbing in Chippendale Avenue in Bangor.
“A shocking incident, terrible for this to happen at any time of the year, let alone Christmas Eve.
“Anyone with any info that can help the police, do provide this ASAP.”