But he said there were still "gaps in our understanding" of the plot, as investigators probed Abedi's potential links to jihadis in Britain, Europe, Libya and the Middle East.
Manchester police arrested a man reported to be Abedi's brother. Prior to the pictures being released, Home Secretary Amber Rudd, referred to the leaking of Abedi's name in the American media before it was publicly released as "irritating". The two leaders will meet at a North Atlantic Treaty Organisation summit in Brussels later on Thursday.
US and British intelligence officials have said that the explosive had a level of sophistication that suggested a larger network.
US media outlets have been reporting details about the attack that British officials hadn't wanted to share yet, to help in their investigation.
Specifically, under the Five Eyes Intelligence agreement, the information is shared with the U.S., Canada, Australia and New Zealand.
The Times story was published after Rudd rebuked the US for naming of suspected suicide bomber hours before United Kingdom authorities were ready to share it. Police hit out on Wednesday at what they said was the publication of evidence in a live investigation.
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The UK terror threat level remains "critical", meaning another attack could be imminent and additional Army and armed police officers are patrolling major sites, including the transport network, across the UK.
Britain's National Counter Terrorism Policing said the U.S. leaks undermined trust between the two countries' intelligence and law enforcement agencies. But when the trust between countries is breached, it harms the investigation, witnesses and victims' families.
"They haven't. Arrogant, wrong and disrespectful to GM [Greater Manchester]", he wrote.
Four days after a suicide bombing left 22 dead and scores wounded at an Ariana Grande concert in Manchester, England, the 23-year-old pop singer has announced that she will return to the grief-stricken city for another concert to benefit the victims and their families.