Twenty individuals detained by police have been repeatedly interviewed and questioned on their links and contacts with the perpetrator of the attack Salman Abedi, the statement added.
Also on Tuesday, police said they had found "significant evidence" in a auto where Abedi may have stored items used to assemble his improvised explosive device.
Jackson said that the 20 people arrested had been interviewed many times, during the course of which "a number" of suspicious purchases of materials that could be used to make explosives were uncovered.
He also praised the "tremendous" work done by Greater Manchester Police crime scene management officers, police family liaison officers, mortuary staff and forensic pathologists.
Libyan official Ahmed bin Salem said that Salman Abedi's brother Hashim was still being held for questioning in Libya.
"Some of those arrested and now released have offered accounts which explain innocent contact with Abedi and we are, at this time, satisfied with these explanations".
More than 1,000 officers have so far been involved in the ongoing investigation, with 8,000 entries on police logging system and at least 700 devices, such as phones, seized for examination.
Police released new images of the R-registration vehicle and appealed for the public's help to locate it on 14 April, when detectives believe it was parked with bomb components inside. He said risk to the public had been considered before suspects were released.
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He said the vast police investigation will continue "as we work to understand the full extent of the involvement of anyone else".
"In such investigations we try to piece together the last movements of the attacker and understand if they were helped". As more information comes in it will be acted upon immediately.
"Our enquiries show that the assembly of the device is likely to have been by Abedi himself", Mr Jackson said.
Det Ch Supt Jackson appealed again for anyone who may have seen Abedi in the days before the attack to come forward - especially those who saw him with the vehicle or putting materials into it.
Detectives believe Abedi assembled the deadly nailbomb himself but have not yet established whether he acted alone in obtaining bomb-making materials before he left the country on 15 April.
A search is also continuing at a landfill site for a blue suitcase which may contain "crucial evidence" that the 22-year-old discarded after assembling the bomb.
"Hashem Abedi, the brother of Salman Abedi, left the country at the same time as the attacker on 15 April".
Police are appealing for anyone who might have seen the white Micra or the barrels to come forward. It was planned carefully and has caused devastation and heartbreak to so many.
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