Police were called to a report that a man had been stabbed at an address on Edleston Street in the town shortly before 1pm on Sunday (January 19).
Officers and paramedics attended the address but despite their efforts the man was pronounced dead at the scene.
He has now been identified as Mark Fisher, 33, who lived at the address.
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His family are aware and are being supported by specially trained officers.
In a tribute Mark’s family said: "As a family we are heartbroken.
"Mark was much loved by all of his family and we miss him so much.
"We desperately need to know what happened to Mark and would appeal to anybody that knows anything to contact the police.”
Two people have now been arrested on suspicion of murder.
They are a 37-year old man and a 35-year-old woman, both from Accrington.
They remain in custody.
Mr Fisher had suffered a number of stab wounds and a Home Office post-mortem examination will be carried out in due course to try to establish the cause of death.
Detectives are continuing to probe the circumstances of the death and are carrying out CCTV enquiries, house to house enquiries and other lines of investigation.
Det Chief Insp Jill Johnston, of the Force Major Investigation Team, is leading the inquiry.
She said: “The incident on Sunday has resulted in a man losing his life and my thoughts are with his family and friends at this time.
“I have a team of detectives and staff working on this investigation and we are following a number of lines of inquiry to piece together what has happened.
“While we have made two arrests our inquiries are still very much ongoing and I would appeal for anyone who has any information which could assist us to come forward.
"Even if you think the information you have is insignificant please come forward and let us be the judge.”
"These rumours are untrue and we would ask people not to repeat them or to speculate."
Police are appealing for any witnesses or anyone who may have information to get in touch.
Anyone with information should contact police on 101 quoting log number 0684 of Sunday, January 19.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555 111.