The family of gunman Derrick Bird say they have no idea why he carried out the "horrific" shootings in Cumbria.
Two statements were read at St Michael's Church in Lamplugh, the village where one of Bird's brothers, his twin, was found dead.
The family also offered condolences to the loved ones of those killed.
Bird's sons Graeme and Jamie said: "We do not know why he committed these horrific crimes and we are both mortified by the sad events."
Later hundreds of people gathered in Seascale, the village where Bird killed three people, for the first of two memorial services.
The second service was held in Whitehaven, where Bird shot dead one of his fellow taxi drivers.
In Lamplugh, in a statement read by Rev Jim Marshall, Bird's sons called the 52-year-old a "loving dad who had recently become a grandfather" and "the nicest man you could ever meet".
They said: "Dad was a loving, cheerful character, and was well known throughout the whole community and the areas in which he worked.
"He will be missed by us and by his family and by his friends."
Of the victims' families, Bird's sons said: "Our thoughts are with them".
Bird killed 12 people in west Cumbria on Wednesday before driving to the Lake District where he shot himself.
Police believe he deliberately targeted some of his victims and indiscriminately shot at others during his 45-mile rampage.
Detectives are continuing to try to establish a motive for the killings.
Speaking outside the church, Mr Marshall said Bird's mother Susan learnt of her son's gun rampage when she turned on the television.
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."
He said Mrs Bird then locked all the doors. When asked if the family had feared for their lives, he replied: "Yes, wouldn't you if you realised (he) had killed his twin brother."
But Mr Marshall said the Derrick Bird his family knew "was not the person they saw on Wednesday".
Bryan Bird, the gunman's surviving brother, also released a statement expressing his "shock and dismay".
He said: "The loss of both of my brothers is devastating. They were both very caring, family people.
"They were well known and respected in their local communities. My family and I are saddened at the loss of life and woundings, and can only offer their condolences to the families concerned.
"We appreciate what they are suffering at this time. We cannot offer any reason why Derrick took it upon himself to commit these crimes."
The President of the Association of Chief Police Officers, Sir Hugh Orde, has praised the response of Cumbria's officers during the shooting spree.
Speaking on the Politics Show on BBC One on Sunday, he said: "It was a completely unexpected and unpredictable event and the response, from a police perspective, was very good."
He said it would not have made any difference if a larger force had been in control.