"We are sure our fans will understand this decision", the team said, adding that the parade would have diverted police from the bombing investigation. Abedi's father and brother were among those arrested, having been detained in Libya.
A "follow-on" attack is possible, the official said.
Another of Abedi's sons, Hashem, was detained on Tuesday evening in Tripoli on suspicion of links to Islamic State, said Ahmed Bin Salem, a spokesman for the Special Deterrence Force, also known as Rada.
On Monday, a suicide bomber killed at least 22 people at a packed concert hall in Manchester, in what British Prime Minister Theresa May called a sickening act targeting children and young people.
Abedi was reported on Wednesday to have been a college dropout who had recently become radicalized.
Shows Thursday and Friday in London were canceled, along with concerts through June 5 in Belgium, Poland, Germany and Switzerland.
The terrorist attack was the worst to strike Britain since the "7/7 attacks" of July 7, 2005, carried out by al Qaeda operatives who targeted buses and subway stations in central London, leaving 56 people dead and more than 700 wounded. They announced no reason for or result of the explosion. Police say he was part of a network and they are racing to track down his links.
Manchester police arrested five men and one woman on Wednesday, bringing the total held for questioning to seven. The identities of those arrested and any charges against them have not been revealed.
Meanwhile, Take That are to stage a stadium show in their native Manchester, England to make up for the three nights they scrapped in the city.
United Kingdom police raced to close down a network around the Manchester suicide bomber on Thursday, as a row escalated between London and Washington over material from the probe leaked to U.S. media.
Two people have been released without being charged, Greater Manchester police said.
Across London, troops fanned out and authorities reconsidered security plans. "We are carrying out extensive searches". Officers also raided a property in the city's Moss Side neighborhood early Thursday and carried out a controlled explosion. "There's about eight officers sitting up there".
Dagdoug said Hashem Abedi had confessed to helping his brother prepare the Manchester attack.
"One of the things that public will see potentially, depending on obviously where they live, is that through Operation Temperer this now allows the police to access support from the military".
Those killed in the attack, which targeted a concert by a pop singer whose core fan group is young girls, include 8-year-old Saffie Rose Roussos. Other victims who have been identified range from teenagers to a Polish couple, Angelika and Marcin Klis, who came to the venue to pick up their daughters.
The U.K.is now at its highest terrorist threat level of "critical" for the first time since 2007. "But an informed understanding of the causes of terrorism is an essential part of an effective response that will protect the security of our people, that fights rather than fuels terrorism". "All our work is created to make our city as hostile an environment as possible for terrorists to plan and operate".
Police and security services are also upset that the name of bomber Salman Abedi was apparently leaked by USA officials and published while police in Britain were withholding the name for what they said were reasons of operational security.