A man and woman were injured in the attack in Bangor on Wednesday afternoon.
Both were taken to hospital. The PSNI initially said one was critically injured.
The suspect, who was armed with a hammer and a knife, remains at large, with the public being warned not to approach him.
One local councillor said it was “shocking and terrible”.
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.
Emergency services at the scene of a double stabbing in the Chippendale Avenue area of Bangor. Photo by Kevin Scott
The Air ambulance also attended the scene.
In an update on Thursday afternoon, 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.”