The terror group has claimed responsibility, but British and USA intelligence have not confirmed that.
Abedi's brother, Hashem, had been "under surveillance for a month and a half", and "investigation teams supplied intelligence that he was planning a terrorist attack in the capital Tripoli", the Special Deterrence Force said on its Facebook page.
"We take full responsibility for that and obviously regret that that happened", the secretary of state told reporters.
"Manchester is a busy place and this weekend we have the Manchester Games, the Great Manchester Run, the Courteeners concert and the start of Ramadan", Greater Manchester Police Chief Constable Ian Hopkins said.
The Manchester attack has caused revulsion across the world because it targeted children and teenagers, who make up the bulk of Grande's fan base. She was scheduled to perform in London Thursday and Friday.
Greater Manchester Police condemned the leaks on behalf of the National Counterterrorism Policing units in a statement that suggested a severe rupture in trust between Britain and the United States, whose law enforcement officials have traditionally shared intelligence at the highest levels.
French Interior Minister Gerard Collomb said Abedi had "likely" been to Syria after Libya, citing information provided by British intelligence services to their counterparts in Paris.
Police confirmed Abedi, 22, was behind the attack.
Grande did not announce when she'll return to Manchester, but promised she'd let fans know as soon as the dates are made official.
Hundreds of people filled central Manchester's St Ann's Square, where flowers and other tributes were laid to remember the victims, with messages including "We stand together" and "We love you".
Numerous victims were children and teenagers - with the youngest of the dead revealed to be just eight-years-old. Dozens more who were injured remain hospitalized, more than 20 of them are listed in critical condition.