The Rev Jim Marshall, curate of St Michael's Church in Lamplugh, Cumbria, spoke of the "dreadful sorrow" felt by Bird's family as he led a service to remember the dead. In a statement read out by Mr Marshall, the killer's sons Graeme and Jamie said they had no idea how their "loving dad" could commit such "horrific crimes".
"We are utterly devastated about the death of our father Derrick Bird," they said. "To us, he was the nicest man you could ever meet. He was a loving dad and recently became a grandfather. We would like to say that we do not know why our dad committed these horrific crimes. We are both mortified by these sad events."
Bird's brother Brian also issued a statement describing the killer and his murdered brother David as a "caring, family people".
The family's description of Bird was met with disbelief by some locals still coming to terms with the massacre, however, with one saying there were "no excuses" for the murders.
Detailing how an ordinary day turned to tragedy last Wednesday, Mr Marshall said Bird's 90-year-old mother Mary found out about his killing spree while watching the one o'clock news on TV.
He said: "She was horrified, she was astounded. She was just stunned and still can't take it in. That is the last time she watched the television. She doesn't want to turn the TV on now."
The 52-year-old Bird murdered 12 people and injured 11 – shooting many of his victims in the face – before taking his own life. Among those murdered was his twin brother David.
Mr Marshall explained how the family feared they might be next to be killed when they realised what was going on.
"Wouldn't you?" he said, "if you realised your brother had killed his twin brother."
Speaking of the Bird family's agony, Mr Marshall said: "If they had the strength to do it, they were the sort of people who would have gone round to each one of the families of people killed and wounded to apologise. That is the strength of their feelings."
He added: "They are sorry for what has happened. There is a millstone around Derrick's name, that isn't the millstone around their neck. It is not their fault. The family are taking on some of that dreadful, dreadful responsibility."
Mr Marshall said the Bird family, whom he has known for many years, had previously been regarded as close, with no hint of the murderous events that were to unfold.
"They have no idea why Derrick did this."
He said the family had at one stage considered a joint funeral for both twins – but this was not going to happen.
Asked to describe Bird, Mr Marshall added: "He was a quiet man but a caring man. He was personable and caring."
However, there was an angry response to the family's comments defending Bird from people in Cumbria last night.
One woman told a local newspaper: "This man had no excuses. He made an informed and selfish choice to kill. He had probably decided to end himself that day, and to take as many people that he 'blamed' for his misfortunes as possible.
"Cruel, cruel, small-minded, selfish, ignorant, pointless man."
The Bird family statements were released as communities gathered across Cumbria for memorial services to remember those who died. An open air service took place in Seascale where Bird killed Michael Pike, 64, Jane Robinson, 66, and Jamie Clark, 23. In nearby Gosforth he shot dead Garry Purdham, 31.
More than 400 local people endured torrential rain to take part in the emotional ceremony.
The Rev Philip Peacock, the minister at Seascale Methodist Church, said: "We wanted to be outside so that the service was accessible to everyone – irrespective of the weather – and we did not want to be locked away in a church."
Yesterday evening another service was held at St Nicholas' Church in Whitehaven, where cabbie Darren Rewcastle died.
More than 1,000 local people attended the evening vigil and Prince Charles sent a message of condolence and support.
The Prince of Wales, who has "great affection for Cumbria", wrote: "My wife and I were utterly horrified to learn of the dreadful events which took place in Cumbria…
"We would be so grateful if you could somehow convey our deepest condolences and heartfelt sympathy to the poor families whose lives have been torn apart in such gravely tragic circumstances. Our hearts go out to Cumbria."
The Rev John Bannister, rector of Whitehaven, said: "The shock hasn't passed. There's a veneer of normality, but beneath that veneer there's a very palpable sense of disbelief. A lot of people are feeling anxious and concerned."
Parishioners in Haile remembered James and Jennifer Jackson, shot dead in the nearby village of Wilton.
Mrs Jackson, 68, and her husband, 67, would normally have been taking communion yesterday in the stone-walled Haile Parish Church.
The Rev Barbara Jeapes told parishioners:
"We thought we were battered before but we realise that we now have a new dimension," she said, referring to an awful year for the county – devastated by floods and heartbroken by the deaths of two pupils and a pensioner in a horrific road crash last week.
"This is a community wound, not an individual wound.
"It is good we are all here today to share that. It is a time for sharing and supporting each other."
Police are still trying to find out what caused Bird's murderous rampage.
They have confirmed the self-employed cabbie was the subject of an Inland Revenue investigation and friends say he feared going to jail over a mystery 60,000 in his bank account.
The will of his father Joe revealed his twin brother David had received a 25,000 payout but he had been ignored.