"We are following up on the network, rolling it up, trying to contain it. As you've seen from the number of arrests, we are on the right track to try to contain it," UK Security Minister Ben Wallace told CNN in Manchester on Friday. "In the end, you get to the bottom of a network."
Investigators continue to work around the clock to track down associates of Abedi, a 22-year-old Briton of Libyan descent, amid fears he is part of a network plotting further mayhem.
On Friday, authorities arrested a man from Manchester's Rusholme neighborhood.
Then, two more men were arrested early Saturday, police said in a statement. The men were taken into custody after officers carried out a controlled explosion to enter a home in the Cheetham Hill area of central Manchester.
Those actions brought the total number of people arrested in the investigation to 13, with 11 still in custody.
Two people have been released without being charged, Greater Manchester police said.
His younger brother, Hashim Ramadan Abu Qassem al-Abedi -- detained in Libya in the aftermath of the bombing -- knew of his brother's movements and about the plot, Ahmed Ben Salem, spokesman for the Special Deterrence Force in Tripoli, told the private broadcaster, Libya's Channel, on Thursday night.
The brothers spoke on the phone just minutes before the attack at a concert at Manchester Arena, Ben Salem said, but Hashim told his Libyan interrogators that he did not know details about where and when the blast would be.
The Special Deterrence Force in Tripoli, a militia nominally under the control of Libya's interior ministry, arrested Hashim al-Abedi a day later on suspicion of links to ISIS. The militia also arrested the brothers' father, Ramadan al-Abedi.
Earlier this week the militia said Hashim had admitted -- under interrogation -- that he and Salman were members of ISIS. It also said Hashim was in Manchester during the planning for the attack and that he had been aware of the plot.
Salman Abedi entered Libya on April 19 and left on May 17, telling his family that he was going to Saudi Arabia to perform the Umrah pilgrimage, Ben Salem told Libya's Channel. It was a deception, and only his brother Hashim knew that Salman actually returned to the UK, according to Ben Salem.
Asked if there was any indication Salman Abedi had received training in Libya or planned an attack inside Libya, Ben Salem said, "I don't think so." Based on what the bomber's brother has told the militia, "everything was prepared in Manchester" since the end of 2016, he said.
US officials told CNN this week that it is likely Salman Abedi received some ISIS training by traveling to Syria in the months before the bombing, according to information gathered in the preliminary investigation.
Monday's attack on concert-goers leaving an Ariana Grande show killed 22 people, many of them children,
and injured dozens more.
In her first comments since the attack, Grande said Friday in a note on Twitter that she is sorry for the "pain and fear" her fans are feeling. She said the fans killed Monday will be on her mind and in her heart forever.
"I will think of them with everything I do for the rest of my life," said the singer, who also announced Friday that she will hold a benefit concert in honor of the victims
of the Manchester attack.
As police raids continued Friday, specially-trained firearms officers were being assigned patrol duty on trains for the first time in Britain. The UK threat level is at its highest level, meaning another attack may be imminent.
British authorities have stopped and disrupted five plots since March 22, when a terror attack outside Parliament in London left five people dead, said Wallace, the security minister. "There are over 400 investigations currently ongoing by the security services and police into terrorist planning or people thinking about terrorist planning."
Meanwhile, Prime Minister Theresa May said she and other leaders at G7 summit in Italy agreed Friday that the threat from ISIS "is revolving, rather than disappearing."
"As they lose ground in Iraq and Syria, foreign fighters are returning, and the group's hateful ideology is spreading online," May told reporters at the summit.
"Make no mistake: The fight is moving from the battlefield to the Internet," she added.
She said the G7 would press tech companies to develop abilities to identify "extremist material and hateful propaganda," remove the material automatically, and report such content to authorities.
May and US President Donald Trump "noted that there had been strong agreement in discussions so far that the G7 should do more collectively on counter terrorism," Downing Street said in a statement.
Corbyn: War on terror 'not working'
Jeremy Corbyn, leader of the Labour Party, the official opposition to the British government, drew a link between UK foreign policy and terror attacks as the main political parties resumed general election campaigning Friday, following the Manchester attack.
Saying the war on terror "is simply not working," Corbyn urged national unity but also said the government must ensure "that our foreign policy reduces rather than increases the threat to this country."
Corbyn, who has a long record of voting against UK military intervention overseas, said a Labour government would "change what we do abroad" if elected, while acknowledging that no government can prevent every attack and that terrorism has many causes.
"Many experts, including professionals in our intelligence and security services have pointed to the connections between wars we have been involved in or supported and and fought in other countries, such as Libya, and terrorism here at home," he said.
"That assessment in no way reduces the guilt of those who attack our children," he said. "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."
May, at the G7 summit, took exception.
"I want to make one thing very clear to Jeremy Corbyn and to you, and it is that there can never, ever be an excuse for terrorism," May said. "There can be no excuse for what happened in Manchester."
She continued, "And I think that this choice that people face in the general election has just become starker. It's a choice between me, working constantly to protect the national interest ... and Jeremy Corbyn, who frankly isn't up to the job."
Row over US leaks
May's discussion with G7 leaders Friday, including Trump, comes on the heels of a spat with the United States over the leaking of intelligence
to US media of details around the Manchester bombing investigation.
The leaks culminated in the New York Times publishing crime scene photos
. Britain responded Thursday by temporarily halting intelligence sharing on the investigation with the United States.
Amid efforts to soothe jangled nerves, US Secretary of State Rex Tillerson arrived in London Friday on his first official visit to Britain,
meeting with his UK counterpart Boris Johnson
and signing a book of condolence for the Manchester victims.
Tillerson said the United States took full responsibility for the leaks, adding that the "special relationship that exists between our two countries will certainly withstand this particular unfortunate event."