The public is being urged to help police piece together the Manchester bomber's final movements as his cousins claimed he plotted "secretly to himself".
New CCTV images have been released showing Salman Abedi moving about the city's streets and hauling a blue suitcase in the days leading up to the Manchester Arena terror attack which killed 22 people.
The developments came as "unscrupulous" ticket touts attempted to profit from Ariana Grande's One Love Manchester gig to raise money for the victims.
Detective Chief Superintendent Russ Jackson, head of the North West Counter Terrorism Unit, said "significant progress" was being made in the investigation, but added that police were still trying to establish why Abedi went to the Banff Road area in Rusholme.
Meanwhile, following claims that warnings about Abedi were not followed up, officers have been unable to find any records of calls to the police anti-terrorist hotline regarding the 22-year-old before the events of May 22.
Brothers Isaac and Abz Forjani, who were arrested by armed police soon after the attack before being released without charge, said they had been left "traumatised" by their cousin's actions.
Abz, 21, told the BBC: "For people who have seen it as a big network we were involved in, it was nothing like that.
"I believe it was all done by one man which developed some sort of thoughts in the past few years which he kept secretly to himself.
"He never shared it with any members of the family - if he would have we could have done something to stop that happening."
Isaac, 24, added: "It's not easy being connected to 22 lost, innocent lives.
"The fact that the person that did this is related to us by blood is something that's going to stay with me for the rest of my life.
"My thoughts are with the families of the victims. I really do feel for them."
They said they last saw Abedi three months before the attack at the younger brother's barber shop.
Overnight, tickets for the upcoming benefit gig appeared for auction online at several times their face value.
One eBay seller was looking to offload four tickets to the gig for £1,250 - which would net a potential profit of nearly £1,100 - but the listing was taken down shortly after being seen by the Press Association.
Official seller Ticketmaster also said more than 25,000 people had applied for free tickets set aside for the 14,200 people who attended the pop star's targeted gig last week, meaning more than 10,000 were "unscrupulous applications".
The police have made Abedi's preparations for the attack the focus of their investigation and, speaking about the new CCTV images, Mr Jackson said: "We are still working to track the movements of Salman Abedi and have already released a number of images of him, in the hope that they will jog people's memories.
''We know that Abedi left the country on April 15 and arrived back on May 18 and we now know from our inquiries that he purchased parts for the bomb after arriving back.
''What we still need to understand is if he had any of the bomb parts in his possession before he went out of the country, this is why we are tracking his movements so carefully."
Mr Jackson said officers had been conducting house-to-house inquiries in the Banff Road area in Rusholme but were "still not satisfied" why Abedi went there and said it was "vital" they understood exactly where he went and who he spoke to in the final days before the attack.
He added: ''Did you see Abedi in the Rusholme area between 18 and 22 May? Do you have any information about his movements on these dates?
''You may think it's insignificant, but it could be a key piece of information to assist us. We need your help as we piece together what happened in the lead-up to the attack and if Abedi was helped by anyone."
Ten men, aged between 18 and 44, remain in custody on suspicion of offences contrary to the Terrorism Act, Greater Manchester Police said.
Six people - including a 15-year-old boy, a 34-year-old woman and four men - have been released without charge after being arrested by officers investigating the attack.
Earlier this week, police released further details about Abedi, including that he had bought most of the key component parts of the suicide bomb in the few days before the attack.
Many of his movements and actions in the four days after his return to the UK from Libya leading up to the May 22 atrocity were also carried out alone but detectives have not ruled out that he was part of "a wider network".
Meanwhile, about 600 stewards will be on duty at Sunday's benefit concert, according to Greater Manchester's police chief, who said security on leaving music events and football matches would have to be reviewed.